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 Equations 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 Equations 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 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 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 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/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/v/solving-equations-2 2023-09-21T22:20:18.864150437Z 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. Sal Khan video https://cdn.kastatic.org/googleusercontent/NW5p7h7ViFUcsKGBcschM9zdOmYIHqwvwvhrnLn_p7sn_hV-eutPUtfFTyfpU-kL1y8Zbgg9jQAxw5SmqkED2LEj_A 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. https://cdn.kastatic.org/ka-youtube-converted/1c5HY3z4k8M.mp4/1c5HY3z4k8M.mp4 246 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/v/solving-equations-with-the-distributive-property 2023-09-15T05:13:15.999416188Z Equations with parentheses When an equation such as -9 - (9x - 6) = 3(4x + 6) has parentheses, we can distribute without changing the value of each side. Then combine like terms. Next, we move all the x-terms to one side and the constants to the other. Finally, we solve for x.  Sal Khan video https://cdn.kastatic.org/googleusercontent/5_hwfcuOOLM4qpRpKxyMDrmM_ivO0AYbRjXw5eWzi74UFuJZPEoAcqhbm6wjY7-VYOQ-ByHDst_nwCw86jOnkaiHig Equations with parentheses When an equation such as -9 - (9x - 6) = 3(4x + 6) has parentheses, we can distribute without changing the value of each side. Then combine like terms. Next, we move all the x-terms to one side and the constants to the other. Finally, we solve for x.  https://cdn.kastatic.org/ka-youtube-converted/YZBStgZGyDY.mp4/YZBStgZGyDY.mp4 364 Equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:num-solutions-linear-equations/v/equation-special-cases 2021-06-21T15:29:05Z Worked example: number of solutions to equations Sal attempts to solve 8(3x + 10) = 28x - 14 - 4x only to find that the equation has no solution. Sal Khan video https://cdn.kastatic.org/googleusercontent/Vqnbb20yMViDTpB8_mVFmW9beu41xEKvZvZy48PWbuo_qwYkkdviLbg5B7d2pXAWWid2tl1O4YCyd__eNrg3pbC3 Worked example: number of solutions to equations Sal attempts to solve 8(3x + 10) = 28x - 14 - 4x only to find that the equation has no solution. https://cdn.kastatic.org/ka-youtube-converted/zKotuhQWIRg.mp4/zKotuhQWIRg.mp4 115 Equations https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/linear-equations-word-problems/v/sum-consecutive-integers 2023-04-19T21:01:17.089483175Z Sums of consecutive integers When solving a math problems involving consecutive integers, we can use algebra to set up an equation to solve for the smallest of the four integers. Sal Khan video https://cdn.kastatic.org/googleusercontent/bppmTTchB8DkQmG8aE0klC9vJpFjEaYx0QaTMhYsQW3GmpHGUUgXp-9YI385qs1zbhdEm_l1mSXtwAiv-l648T5bRw Sums of consecutive integers When solving a math problems involving consecutive integers, we can use algebra to set up an equation to solve for the smallest of the four integers. https://cdn.kastatic.org/ka-youtube-converted/8CJ6Qdcoxsc.mp4/8CJ6Qdcoxsc.mp4 319 Equations https://www.khanacademy.org/math/up-class-9-bridge/x27a9f6658c8b5c27:linear-equations-in-one-variable/x27a9f6658c8b5c27:untitled-16/e/b9-linear-equations-in-one-variable-word-problems 2023-04-19T21:01:17.089483175Z Linear equations in one variable (Word problems) Linear equations in one variable (Word problems) ashish exercise