Elementary equations (advanced practice)

{"questions":[{"content":"Find the root of the equation: $$\\log_2(x+6)=2\\log_211$$[[fill_choice_big-1]][[image-2107]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$115$","$6$","$17$"],"placeholder":0,"answer":0},"image-2107":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/dumaet-01-2.svg","width":"300"}},"step":1,"hints":["On the right side of the equation, we enter the factor $2$ inside the logarithm as a exponent of the argument: $$\\log_2(x+6)=\\log_211^2$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$x+6=11^2$$ $$x=115$$"]},{"content":"Find the root of the equation: $$\\log_5(x-4)=2\\log_515$$[[fill_choice_big-12]][[image-2122]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$229$","$18$","$116$"],"placeholder":0,"answer":0},"image-2122":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/vremya3-01.svg","width":"300"}},"step":1,"hints":["On the right side of the equation, we enter the factor $2$ inside the logarithm as a exponent of the argument: $$\\log_5(x-4)=\\log_515^2$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$x-4=15^2$$ $$x=229$$"]},{"content":"Find the root of the equation: $$\\log_8(5-x)=2\\log_89$$[[fill_choice_big-41]][[image-2139]]","widgets":{"fill_choice_big-41":{"type":"fill_choice_big","options":["$-76$","$0$","$-19$"],"placeholder":0,"answer":0},"image-2139":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/pishet-formuly-na-doske-doska2-01.svg","width":"300"}},"step":1,"hints":["On the right side of the equation, we enter the factor $2$ inside the logarithm as a exponent of the argument: $$\\log_8(5-x)=\\log_8 9^2$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$5-x=9^2$$ $$x=-76$$"]},{"content":"Find the root of the equation: $$\\log_2(x+1)=1+\\log_2 5$$[[fill_choice_big-125]][[image-2158]]","widgets":{"fill_choice_big-125":{"type":"fill_choice_big","options":["$9$","$1$","$5$"],"placeholder":0,"answer":0},"image-2158":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/schety-1.svg","width":"300"}},"step":1,"hints":["Represent the number $1$ as a logarithm with the base $2$: $$\\log_2(x+1)=\\log_2 2+\\log_2 5$$","Find the sum of logarithms with the same bases, using the property of logarithms: $$\\log_2(x+1)=\\log_2 2\\cdot 5$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$x+1=10$$ $$x=9$$"]},{"content":"Find the root of the equation: $$\\log_3(2x-2)=1+\\log_3 10$$[[fill_choice_big-239]][[image-2179]]","widgets":{"fill_choice_big-239":{"type":"fill_choice_big","options":["$16$","$10$","$-6$"],"placeholder":0,"answer":0},"image-2179":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/diagramma-stol-lapy-1.svg","width":"300"}},"step":1,"hints":["Represent the number $1$ as a logarithm with the base $3$: $$\\log_3(2x-2)=\\log_3 3+\\log_3 10$$","Find the sum of logarithms with the same bases, using the property of logarithms: $$\\log_3(2x-2)=\\log_3 3\\cdot 10$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$2x-2=30$$ $$x=16$$"]},{"content":"Find the root of the equation: $$\\log_4(3x+6)=1+\\log_4 12$$[[fill_choice_big-306]][[image-2202]]","widgets":{"fill_choice_big-306":{"type":"fill_choice_big","options":["$14$","$12$","$8$"],"placeholder":0,"answer":0},"image-2202":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/personazh-s-lupoi-1-2.svg","width":"300"}},"step":1,"hints":["Represent the number $1$ as a logarithm with the base $4$: $$\\log_4(3x+6)=\\log_4 4+\\log_4 12$$","Find the sum of logarithms with the same bases, using the property of logarithms: $$\\log_4(3x+6)=\\log_4 4\\cdot 12$$","The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$3x+6=48$$ $$x=14$$"]}]}

{"questions":[{"content":"Find the root of the equation: $$\\log_8(17-x)=\\log_83$$[[fill_choice_big-1]][[image-1468]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$14$","$6$","$0$"],"placeholder":0,"answer":0},"image-1468":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/vnutri-doma-01-1.svg","width":"300"}},"step":1,"hints":["The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$17-x=3$$ $$x=14$$"]},{"content":"Find the root of the equation: $$\\log_5(13-x)=\\log_59$$[[fill_choice_big-11]][[image-1429]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$4$","$9$","$2$"],"placeholder":0,"answer":0},"image-1429":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/11/uchenyi-kletochnaya-membrana-mikroskop-01-01.svg","width":"300"}},"step":1,"hints":["The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$13-x=9$$ $$x=4$$"]},{"content":"Find the root of the equation: $$\\log_2(x+13)=\\log_2(6x-17)$$[[fill_choice_big-36]][[image-1392]]","widgets":{"fill_choice_big-36":{"type":"fill_choice_big","options":["$6$","$4$","$7$"],"placeholder":0,"answer":0},"image-1392":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/12/lawyer-01.svg","width":"300"}},"step":1,"hints":["The left and right sides of the equation have logarithms with the same bases, which means their arguments will be equal: $$x+13=6x-17$$ $$x=6$$"]},{"content":"Find the root of the equation: $$\\log_3(8+x)=4$$[[fill_choice_big-96]][[image-1357]]","widgets":{"fill_choice_big-96":{"type":"fill_choice_big","options":["$73$","$4$","$12$"],"placeholder":0,"answer":0},"image-1357":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/skai-p-za-kompyuterom-sidit-01-1.svg","width":"300"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$8+x = 3^4$$ $$8+x=81$$ $$x=73$$"]},{"content":"Find the root of the equation: $$\\log_4(9-x)=2$$[[fill_choice_big-205]][[image-1324]]","widgets":{"fill_choice_big-205":{"type":"fill_choice_big","options":["$-7$","$6$","$16$"],"placeholder":0,"answer":0},"image-1324":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/shestirenki-01.svg","width":"297"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$9-x = 4^2$$ $$9-x=16$$ $$x=-7$$"]},{"content":"Find the root of the equation: $$\\log_2(3+x)=7$$[[fill_choice_big-262]][[image-1293]]","widgets":{"fill_choice_big-262":{"type":"fill_choice_big","options":["$125$","$49$","$6$"],"placeholder":0,"answer":0},"image-1293":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/ideya-lampochka-01-1.svg","width":"300"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$3+x = 2^7$$ $$3+x=128$$ $$x=125$$"]},{"content":"Find the root of the equation: $$\\log_5(1-x)=-2$$[[fill_choice_big-349]][[image-1264]]","widgets":{"fill_choice_big-349":{"type":"fill_choice_big","options":["$0.96$","$-5$","$3$"],"placeholder":0,"answer":0},"image-1264":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/obrazavr-v-kruge-kvadrate-01-01.svg","width":"300"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$1-x = 5^{-2}$$ $$1-x=\\frac{1}{25}$$ $$x=0.96$$"]},{"content":"Find the root of the equation: $$\\log_{\\frac{1}{3}}(6-x)=-4$$[[fill_choice_big-514]][[image-1237]]","widgets":{"fill_choice_big-514":{"type":"fill_choice_big","options":["$-75$","$12$","$-4$"],"placeholder":0,"answer":0},"image-1237":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/uchenyi-dissertatsiya-papka.svg","width":"297"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$6-x = \\Big(\\frac{1}{3}\\Big)^{-4}$$ $$6-x=81$$ $$x=-75$$"]},{"content":"Find the root of the equation: $$\\log_{\\frac{1}{2}}(9+x)=-3$$[[fill_choice_big-663]][[image-1212]]","widgets":{"fill_choice_big-663":{"type":"fill_choice_big","options":["$-1$","$2$","$8$"],"placeholder":0,"answer":0},"image-1212":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/computer-games-1.svg","width":"300"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$9+x = \\Big(\\frac{1}{2}\\Big)^{-3}$$ $$9+x=8$$ $$x=-1$$"]},{"content":"Find the root of the equation: $$\\log_{\\frac{1}{9}}(x+12)=-2$$[[fill_choice_big-786]][[image-1189]]","widgets":{"fill_choice_big-786":{"type":"fill_choice_big","options":["$69$","$12$","$-81$"],"placeholder":0,"answer":0},"image-1189":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/uchenye_himiya-06-01.svg","width":"300"}},"step":1,"hints":["The logarithm is equal to the power to which the base must be raised to obtain the argument: $$x+12 = \\Big(\\frac{1}{9}\\Big)^{-2}$$ $$x+12=81$$ $$x=69$$"]}]}

{"questions":[{"content":"Find the root of the equation: $$5^{x+6}=125$$[[fill_choice_big-1]][[image-538]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$-3$","$125$","$6$"],"placeholder":0,"answer":0},"image-538":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/sidyat-za-partoj-ruchka.svg","width":"300"}},"step":1,"hints":["Represent the number $125$ as $5$ to the power $3$:$$5^{x+6}=5^3$$","The bases are equal, so the exponents are equal: $$x+6=3$$ $$x=-3$$"]},{"content":"Find the root of the equation: $$3^{x-6}=729$$[[fill_choice_big-16]][[image-499]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$12$","$0$","$6$"],"placeholder":0,"answer":0},"image-499":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/12/ruchka-ezhednevnik.svg","width":"298"}},"step":1,"hints":["Represent the number $729$ as $3$ to the power $6$:$$3^{x-6}=3^6$$","The bases are equal, so the exponents are equal: $$x-6=6$$ $$x=12$$"]},{"content":"Find the root of the equation: $$5^{x-40}=625$$[[fill_choice_big-69]][[image-462]]","widgets":{"fill_choice_big-69":{"type":"fill_choice_big","options":["$44$","$26$","$6$"],"placeholder":0,"answer":0},"image-462":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/12/book.svg","width":"303"}},"step":1,"hints":["Represent the number $625$ as $5$ to the power $4$:$$5^{x-40}=5^4$$","The bases are equal, so the exponents are equal: $$x-40=4$$ $$x=44$$"]},{"content":"Find the root of the equation: $$6^{2x-12}=36$$[[fill_choice_big-126]][[image-427]]","widgets":{"fill_choice_big-126":{"type":"fill_choice_big","options":["$7$","$5$","$0$"],"placeholder":0,"answer":0},"image-427":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/01/tetrad-lastik-penal-uchebnik-pishet-.svg","width":"299"}},"step":1,"hints":["Represent the number $36$ as $6$ to the power $2$:$$6^{2x-12}=6^2$$","The bases are equal, so the exponents are equal: $$2x-12=2$$ $$x=7$$"]},{"content":"Find the root of the equation: $$2^{3x+8}=256$$[[fill_choice_big-171]][[image-394]]","widgets":{"fill_choice_big-171":{"type":"fill_choice_big","options":["$0$","$8$","$4$"],"placeholder":0,"answer":0},"image-394":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2025/05/do-homework_2-01.svg","width":"300"}},"step":1,"hints":["Represent the number $256$ as $2$ to the power $8$:$$2^{3x+8}=2^8$$","The bases are equal, so the exponents are equal: $$3x+8=8$$ $$x=0$$"]},{"content":"Find the root of the equation: $$2^{x+2}=\\frac{1}{64}$$[[fill_choice_big-303]][[image-363]]","widgets":{"fill_choice_big-303":{"type":"fill_choice_big","options":["$-8$","$5$","$4$"],"placeholder":0,"answer":0},"image-363":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/shkolniki-klass-party-parta-okno-stulya-stoly-sidyat-za-partoi-.svg","width":"300"}},"step":1,"hints":["Represent the number $\\frac{1}{64}$ as $2$ to the power $-6$:$$2^{x+2}=2^{-6}$$","The bases are equal, so the exponents are equal: $$x+2=-6$$ $$x=-8$$"]},{"content":"Find the root of the equation: $$16^{x-5}=\\frac{1}{64}$$[[fill_choice_big-396]][[image-334]]","widgets":{"fill_choice_big-396":{"type":"fill_choice_big","options":["$3.5$","$6$","$-2$"],"placeholder":0,"answer":0},"image-334":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/09/klass-parta-uchitel-uchenik.svg","width":"300"}},"step":1,"hints":["Let us represent the number $16$ as $4$ to the power of $2$, and the number $\\frac{1}{64}$ as $4$ to the power of $-3$:$$(4^2)^{x-5}=4^{-3}$$ $$4^{2x-10}=4^{-3}$$","The bases are equal, so the exponents are equal: $$2x-10=-3$$ $$2x=7$$ $$x=3.5$$"]},{"content":"Find the root of the equation: $$\\Big(\\frac{1}{7}\\Big)^{5-7x}=49$$[[fill_choice_big-547]][[image-307]]","widgets":{"fill_choice_big-547":{"type":"fill_choice_big","options":["$1$","$0$","$-7$"],"placeholder":0,"answer":0},"image-307":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/read.svg","width":"298"}},"step":1,"hints":["Represent the number $49$ as $\\frac{1}{7}$ to the power $-2$:$$\\Big(\\frac{1}{7}\\Big)^{5-7x}=\\Big(\\frac{1}{7}\\Big)^{-2}$$","The bases are equal, so the exponents are equal: $$5-7x=-2$$ $$x=1$$"]},{"content":"Find the root of the equation: $$\\Big(\\frac{1}{2}\\Big)^{x+2}=\\frac{1}{16}$$[[fill_choice_big-688]][[image-282]]","widgets":{"fill_choice_big-688":{"type":"fill_choice_big","options":["$2$","$4$","$-2$"],"placeholder":0,"answer":0},"image-282":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/sitting-on-books-v2.svg","width":"300"}},"step":1,"hints":["Represent the number $\\frac{1}{16}$ as $\\frac{1}{2}$ to the power $4$:$$\\Big(\\frac{1}{2}\\Big)^{x+2}=\\Big(\\frac{1}{2}\\Big)^4$$","The bases are equal, so the exponents are equal: $$x+2=4$$ $$x=2$$"]},{"content":"Find the root of the equation: $$\\Big(\\frac{1}{4}\\Big)^{x+5}=256$$[[fill_choice_big-847]][[image-259]]","widgets":{"fill_choice_big-847":{"type":"fill_choice_big","options":["$-9$","$-4$","$0$"],"placeholder":0,"answer":0},"image-259":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/04/chitaet-knigi-sidit-za-partoj-parta-1.svg","width":"300"}},"step":1,"hints":["Represent the number $256$ as $\\frac{1}{4}$ to the power $-4$:$$\\Big(\\frac{1}{4}\\Big)^{x+5}=\\Big(\\frac{1}{4}\\Big)^{-4}$$","The bases are equal, so the exponents are equal: $$x+5=-4$$ $$x=-9$$"]}]}

{"questions":[{"content":"Find the root of the equation: $$\\sqrt{37-4x}=6$$[[fill_choice_big-1]][[image-742]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$0.25$","$5$","$37$"],"placeholder":0,"answer":0},"image-742":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2025/09/ekonomika-01.svg","width":"300"}},"step":1,"hints":["Square both sides of the equation to get rid of the root: $$(\\sqrt{37-4x})^2=6^2$$ $$37-4x=36$$ $$-4x=-1$$ $$x=0.25$$"]},{"content":"Find the root of the equation: $$\\sqrt{25-3x}=2$$[[fill_choice_big-24]][[image-783]]","widgets":{"fill_choice_big-24":{"type":"fill_choice_big","options":["$7$","$5$","$11$"],"placeholder":0,"answer":0},"image-783":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/dumaet-nad-formulami-na-doske-formuly-doska.svg","width":"300"}},"step":1,"hints":["Square both sides of the equation to get rid of the root: $$(\\sqrt{25-3x})^2=2^2$$ $$25-3x=4$$ $$-3x=-21$$ $$x=7$$"]},{"content":"Find the root of the equation: $$\\sqrt{37-2x}=5$$[[image-828]][[fill_choice_big-58]]","widgets":{"image-828":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/konferentsiya-01-3.svg","width":"300"},"fill_choice_big-58":{"type":"fill_choice_big","options":["$6$","$5$","$-7$"],"placeholder":0,"answer":0}},"step":1,"hints":["Square both sides of the equation to get rid of the root: $$(\\sqrt{37-2x})^2=5^2$$ $$37-2x=25$$ $$-2x=-12$$ $$x=6$$"]},{"content":"Find the root of the equation: $$\\sqrt{9x+19}=8$$[[fill_choice_big-47]][[image-877]]","widgets":{"fill_choice_big-47":{"type":"fill_choice_big","options":["$5$","$9$","$19$"],"placeholder":0,"answer":0},"image-877":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/05/kniga_obrazavr-01.svg","width":"300"}},"step":1,"hints":["Square both sides of the equation to get rid of the root: $$(\\sqrt{9x+19})^2=8^2$$ $$9x+19=64$$ $$9x=45$$ $$x=5$$"]},{"content":"Find the root of the equation: $$\\sqrt{38x+45}=11$$[[fill_choice_big-89]][[image-930]]","widgets":{"fill_choice_big-89":{"type":"fill_choice_big","options":["$2$","$40$","$11$"],"placeholder":0,"answer":0},"image-930":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/05/obrazavr_deyatelnost_dop-04-2.svg","width":"300"}},"step":1,"hints":["Square both sides of the equation to get rid of the root: $$(\\sqrt{38x+45})^2=11^2$$ $$38x+45=121$$ $$38x=76$$ $$x=2$$"]},{"content":"Find the root of the equation: $$\\sqrt[5]{x-7}=2$$[[fill_choice_big-138]][[image-1015]]","widgets":{"fill_choice_big-138":{"type":"fill_choice_big","options":["$39$","$11$","$85$"],"placeholder":0,"answer":0},"image-1015":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/question-mark.svg","width":"300"}},"hints":["Raise both sides of the equation to the fifth power to get rid of the root: $$(\\sqrt[5]{x-7})^5=2^5$$ $$x-7=32$$ $$x=39$$"]},{"content":"Find the root of the equation: $$\\sqrt[3]{x+4}=5$$[[fill_choice_big-210]][[image-1046]]","widgets":{"fill_choice_big-210":{"type":"fill_choice_big","options":["$121$","$5$","$-16$"],"placeholder":0,"answer":0},"image-1046":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/istorik-istoriya-chitaet-knigu-kniga-lupa-01.svg","width":"300"}},"step":1,"hints":["Raise both sides of the equation to the third power to get rid of the root: $$(\\sqrt[3]{x+4})^3=5^3$$ $$x+4=125$$ $$x=121$$"]},{"content":"Find the root of the equation: $$\\sqrt[5]{x-6}=3$$[[fill_choice_big-321]][[image-1079]]","widgets":{"fill_choice_big-321":{"type":"fill_choice_big","options":["$249$","$129$","$-219$"],"placeholder":0,"answer":0},"image-1079":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/golosovanie-01-2.svg","width":"303"}},"step":1,"hints":["Raise both sides of the equation to the fifth power to get rid of the root: $$(\\sqrt[5]{x-6})^5=3^5$$ $$x-6=243$$ $$x=249$$"]},{"content":"Find the root of the equation: $$\\sqrt[7]{2x-8}=2$$[[fill_choice_big-444]][[image-1114]]","widgets":{"fill_choice_big-444":{"type":"fill_choice_big","options":["$68$","$14$","$-15$"],"placeholder":0,"answer":0},"image-1114":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2026/01/teacher.svg","width":"300"}},"step":1,"hints":["Raise both sides of the equation to the seventh power to get rid of the root: $$(\\sqrt[7]{2x-8})^7=2^7$$ $$2x-8=128$$ $$2x=136$$ $$x= 68$$"]},{"content":"Find the root of the equation: $$\\sqrt[3]{5x-6}=4$$[[fill_choice_big-569]][[image-1151]]","widgets":{"fill_choice_big-569":{"type":"fill_choice_big","options":["$14$","$52$","$-4$"],"placeholder":0,"answer":0},"image-1151":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/05/shestirenka2-02.svg","width":"300"}},"step":1,"hints":["Raise both sides of the equation to the third power to get rid of the root: $$(\\sqrt[3]{5x-6})^3=4^3$$ $$5x-6=64$$ $$5x=70$$ $$x= 14$$"]}],"mix":1}

{"questions":[{"content":"Find the root of the equation:$$\\frac{1}{3x-4}=\\frac{1}{11}$$[[fill_choice_big-1]][[image-16]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$3$","$11$","$5$"],"placeholder":0,"answer":2},"image-16":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/12/lysyj-01.svg","width":"200"}},"step":1,"hints":["The numerators of the fractions are equal, which means the denominators will also be equal: $$3x-4=11$$","$$3x-4=11$$ $$3x=15$$ $$x=5$$"]},{"content":"Find the root of the equation:$$\\frac{1}{2x+13}=\\frac{1}{5}$$[[fill_choice_big-2]][[image-51]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$-4$","$2$","$-0.5$"],"placeholder":0,"answer":0},"image-51":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/na-rabotu-2.svg","width":"200"}},"step":1,"hints":["The numerators of the fractions are equal, which means the denominators will also be equal: $$2x+13=5$$","$$2x+13=5$$ $$2x=-8$$ $$x=-4$$"]},{"content":"Find the root of the equation:$$\\frac{1}{4x-6}=\\frac{1}{10}$$[[fill_choice_big-225]][[image-272]]","widgets":{"fill_choice_big-225":{"type":"fill_choice_big","options":["$4$","$5$","$-2$"],"placeholder":0,"answer":0},"image-272":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/02/student-uchenik.svg","width":"200"}},"step":1,"hints":["The numerators of the fractions are equal, which means the denominators will also be equal: $$4x-6=10$$","$$4x-6=10$$ $$4x=16$$ $$x=4$$"]},{"content":"Find the root of the equation:$$\\frac{1}{3x-10}=5$$[[fill_choice_big-387]][[image-142]]","widgets":{"fill_choice_big-387":{"type":"fill_choice_big","options":["$3.4$","$5.6$","$7$"],"placeholder":0,"answer":0},"image-142":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/convo-dinos.svg","width":"200"}},"step":1,"hints":["Multiply the left and right sides of the equation by $3x-10,$ to get rid of the denominator: $$1=5(3x-10)$$","$$1=5(3x-10)$$ $$1=15x-50$$ $$15x=51$$ $$x=3.4$$"]},{"content":"Find the root of the equation:$$\\frac{x-98}{x+18}=3$$[[fill_choice_big-531]][[image-199]]","widgets":{"fill_choice_big-531":{"type":"fill_choice_big","options":["$-76$","$15$","$185$"],"placeholder":0,"answer":0},"image-199":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/personazh-dumaet.svg","width":"200"}},"step":1,"hints":["Multiply the left and right sides of the equation by $x+18,$ to get rid of the denominator: $$x-98=3(x+18)$$","$$x-98=3(x+18)$$ $$x-98=3x+54$$ $$2x=-152$$ $$x=-76$$"]},{"content":"Find the root of the equation: $$(x-9)^3=-27$$[[fill_choice_big-776]][[image-260]]","widgets":{"fill_choice_big-776":{"type":"fill_choice_big","options":["$6$","$9$","$5$"],"placeholder":0,"answer":0},"image-260":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/devochka-devushka-ochki-govorit-stoit-1-1.svg","width":"200"}},"step":1,"hints":["Represent the number $-27$ as a number to the $3$ power: $$(x-9)^3=(-3)^3$$","The powers are equal, which means the bases will also be equal: $$x-9=-3$$ $$x=6$$"]},{"content":"Find the root of the equation: $$(x-5)^3=64$$[[fill_choice_big-899]][[image-325]]","widgets":{"fill_choice_big-899":{"type":"fill_choice_big","options":["$9$","$8$","$5$"],"placeholder":0,"answer":0},"image-325":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/kniga_nauka-chitaet-obrazavr-01-01.svg","width":"200"}},"step":1,"hints":["Represent the number $64$ as a number to the $3$ power: $$(x-5)^3=4^3$$","The powers are equal, which means the bases will also be equal: $$x-5=4$$ $$x=9$$"]},{"content":"Find the root of the equation: $$(x-4)^3=8$$[[fill_choice_big-1036]][[image-394]]","widgets":{"fill_choice_big-1036":{"type":"fill_choice_big","options":["$6$","$4$","$8$"],"placeholder":0,"answer":0},"image-394":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/studyhard.svg","width":"200"}},"step":1,"hints":["Represent the number $8$ as a number to the $3$ power: $$(x-4)^3=2^3$$","The powers are equal, which means the bases will also be equal: $$x-4=2$$ $$x=6$$"]},{"content":"Find the root of the equation: $$(x-43)^5=-243$$[[fill_choice_big-1209]][[image-467]]","widgets":{"fill_choice_big-1209":{"type":"fill_choice_big","options":["$40$","$15$","$-13$"],"placeholder":0,"answer":0},"image-467":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/08/v-ochkah-s-knigoi-kniga-tetrad-pishet-01-2.svg","width":"200"}},"step":1,"hints":["Represent the number $-243$ as a number to the $5$ power: $$(x-43)^5=(-3)^5$$","The powers are equal, which means the bases will also be equal: $$x-43=-3$$ $$x=40$$"]},{"content":"Find the root of the equation: $$(x+17)^3=27$$[[image-37]][[fill_choice_big-58]]","widgets":{"image-37":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/07/obrazavr_with_a_map3-01.svg","width":"200"},"fill_choice_big-58":{"type":"fill_choice_big","options":["$-14$","$12$","$-5$"],"placeholder":0,"answer":0}},"hints":["Represent the number $27$ as a number to the $3$ power: $$(x+17)^3=3^3$$","The powers are equal, which means the bases will also be equal: $$x+17=3$$ $$x=-14$$"]}]}