https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/v/why-we-do-the-same-thing-to-both-sides-multi-step-equations 2021-06-17T13:24:35Z Why we do the same thing to both sides: Variable on both sides We will use a scale to try to achieve balance and help explain why we do the same thing to both sides of an equation, even when the variable appears on both sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/GYAT-fRjJXXP4vqLux5GE3F8jp0GdZ_YEsfj1b2MZPqJ-pM99BKW9vrMvXo_BmjD8Ks8A1-1bvFSECRy8PsDgARCZg Why we do the same thing to both sides: Variable on both sides We will use a scale to try to achieve balance and help explain why we do the same thing to both sides of an equation, even when the variable appears on both sides. https://cdn.kastatic.org/ka-youtube-converted/vkhYFml0w6c.mp4/vkhYFml0w6c.mp4 456 Algebraic equations https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:algebra-and-graphs/x3f4c73d082a798eb:equations/e/b-linear-equations 2023-04-19T21:28:53.788177796Z Linear equations Linear equations ashish exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:num-solutions-linear-equations/v/number-of-solutions-to-linear-equations 2023-09-21T22:20:18.864150437Z Number of solutions to equations A linear equation could have exactly 1, 0, or infinite solutions. If we can solve the equation and get something like x=b where b is a specific number, then we have one solution. If we end up with a statement that's always false, like 3=5, then there's no solution. If we end up with a statement that's always true, like 5=5, then there are infinite solutions. Sal Khan video https://cdn.kastatic.org/googleusercontent/wDWDgdAhE6N556bQvkI9Cmjc6dZutUWeaaXBhgV4gXwE7P7S7S29OhXdcwbXZzQXyIdSKqIKe5z8wi3oQt7v5u_xWw Number of solutions to equations A linear equation could have exactly 1, 0, or infinite solutions. If we can solve the equation and get something like x=b where b is a specific number, then we have one solution. If we end up with a statement that's always false, like 3=5, then there's no solution. If we end up with a statement that's always true, like 5=5, then there are infinite solutions. https://cdn.kastatic.org/ka-youtube-converted/qsL_5Y8uWPU.mp4/qsL_5Y8uWPU.mp4 328 Algebraic equations https://www.khanacademy.org/math/grade-7-math-cambridge/xffb7c9f797a6b534:algebra/xffb7c9f797a6b534:algebraic-equations/e/v1-h6-solving-linear-equations-0 2021-10-15T21:16:58.572783132Z Solving linear equations: Foundations exercise https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-1 2022-11-16T04:22:43.7414897Z Linear equations 1 To solve linear equations, find the value of the variable that makes the equation true. Use the inverse of the number that multiplies the variable, and multiply or divide both sides by it. Simplify the result to get the variable value. Check your answer by plugging it back into the equation. Sal Khan video https://cdn.kastatic.org/googleusercontent/4rKEiu6RdJK_X1KOaqDgtAjtr_tlxr93Mehi1sT6s1mitVwox2Y6lNUuWQS7Wjgh6UoxXDpW0wFOOhWGliHcasA Linear equations 1 To solve linear equations, find the value of the variable that makes the equation true. Use the inverse of the number that multiplies the variable, and multiply or divide both sides by it. Simplify the result to get the variable value. Check your answer by plugging it back into the equation. https://cdn.kastatic.org/ka-youtube-converted/bAerID24QJ0.mp4/bAerID24QJ0.mp4 447 Algebraic equations https://www.khanacademy.org/math/grade-7-math-snc-aligned/xf9992e17a4bae62e:equations-and-inequalities/xf9992e17a4bae62e:solving-linear-equations/e/n-linear-equations-in-one-variable-2-1 2026-03-31T08:52:19.062243676Z Linear equations in one variable 2.1 Linear equations in one variable ashish exercise https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-2 2020-06-23T07:22:43Z Linear equations 2 solving equations of the form AX+B=C Sal Khan video https://cdn.kastatic.org/googleusercontent/TyYfwoZtTlaDYyld6bP_p-n4GMT2VZjMPT1pazIiOlWyRtuzlfiEjsf45eOLbbB2nooOkm05-JjVVy2dvsq2gSXE Linear equations 2 solving equations of the form AX+B=C https://cdn.kastatic.org/ka-youtube-converted/DopnmxeMt-s.mp4/DopnmxeMt-s.mp4 367 Algebraic equations https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-one-step-mult-div-equations/e/linear_equations_1 2026-02-18T21:10:37.070672468Z One-step multiplication & division equations Practice solving equations in one step by multiplying or dividing a value from both sides. Marcia Lee exercise https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-3 2020-06-23T07:22:43Z Linear equations 3 Linear equations with multiple variable and constant terms Sal Khan video https://cdn.kastatic.org/googleusercontent/4nplZ6BYNAMJ-yH1nUyo3gd_51W2rVmNZLUBVcfWjoRF5YLJmqEyMaqxIHk01ryv4RmaPb1aC2Nm3oAZs-A-i1k_ Linear equations 3 Linear equations with multiple variable and constant terms https://cdn.kastatic.org/ka-youtube-converted/Zn-GbH2S0Dk.mp4/Zn-GbH2S0Dk.mp4 405 Algebraic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-parentheses/v/reasoning-with-linear-equations 2022-09-10T01:04:29.754011735Z Reasoning with linear equations When we perform operations to manipulate equations, some operations produce equivalent equations, while others don't necessarily produce equivalent equations. When we're solving an equation, we need to use operations that guarantee equivalence. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/6398c75c-35a0-4a9f-b33f-27c2e63912e6_1280_720_base.png Reasoning with linear equations When we perform operations to manipulate equations, some operations produce equivalent equations, while others don't necessarily produce equivalent equations. When we're solving an equation, we need to use operations that guarantee equivalence. https://cdn.kastatic.org/ka-youtube-converted/BV-TGIMUXaw.mp4/BV-TGIMUXaw.mp4 460 Algebraic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/v/equations-3 2023-09-21T22:20:18.864150437Z Intro to equations with variables on both sides Learn how to solve the equation 2x + 3 = 5x - 2 with the variable on both sides. We start by visualizing the equation, then isolate the variable by performing the same operations on both sides. Finally, we solve the equation to find the value of the variable. Sal Khan video https://cdn.kastatic.org/googleusercontent/bSvSLNTpzUk-WzbidKWo7Ovl-30QAFH5PaF4eubV3eauWGqOHslKdokFcpc2EZlXrzIBgmUsvrTXwqFPAVbeWy_LMg Intro to equations with variables on both sides Learn how to solve the equation 2x + 3 = 5x - 2 with the variable on both sides. We start by visualizing the equation, then isolate the variable by performing the same operations on both sides. Finally, we solve the equation to find the value of the variable. https://cdn.kastatic.org/ka-youtube-converted/f15zA0PhSek.mp4/f15zA0PhSek.mp4 533 Algebraic equations https://www.khanacademy.org/math/up-class-9-bridge/x27a9f6658c8b5c27:linear-equations-in-one-variable/x27a9f6658c8b5c27:untitled-16/e/linear-equations-in-one-variable 2023-03-03T12:49:07.012797194Z Linear equations in one variable Linear equations in one variable ashish exercise https://www.khanacademy.org/math/algebra-1-eureka-squared-aligned/x15446f63b23e2a07:expressions-equations-and-inequalities-in-one-variable/x15446f63b23e2a07:solving-linear-equations-in-one-variable/v/equations-with-variables-on-both-sides-20-7x6x-6-indian-accent 2025-06-08T17:06:50.364590398Z Equations with variables on both sides: 20-7x=6x-6 Solving equations like 20 - 7x = 6x - 6 with the variable on both sides involves a few steps! First, we add or subtract terms from both sides to separate constants and variables to different sides of the equation. Then, we simplify to isolate the variable. Finally, we check our answer by plugging it back into the original equation. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equations with variables on both sides: 20-7x=6x-6 Solving equations like 20 - 7x = 6x - 6 with the variable on both sides involves a few steps! First, we add or subtract terms from both sides to separate constants and variables to different sides of the equation. Then, we simplify to isolate the variable. Finally, we check our answer by plugging it back into the original equation. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by https://cdn.kastatic.org/ka-youtube-converted/0ftMWNI7UGk.mp4/0ftMWNI7UGk.mp4 246 Algebraic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/e/linear_equations_3 2025-02-18T07:52:09.551150445Z Equations with variables on both sides Practice solving one-variable equations like 20 - 7x = 6x - 6, where the variable appears on both sides of the equals sign. Ben Stenhaug exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-parentheses/e/multistep_equations_with_distribution 2025-02-18T07:52:09.551150445Z Equations with parentheses Practice solving equations with parentheses using the distributive property. Ben Stenhaug exercise