This article has been viewed 111,000 times. This is done by reversing the addition or subtraction of one of the terms with the variable. [latex]\frac{8x}{\color{red}{8}}=\frac{24}{\color{red}{8}}[/latex], [latex]7(\color{red}{3})\stackrel{\text{? Now all the [latex]x[/latex] s are on the left and the constant on the right. Solving Equations with a Variable on Both Sides, Solving Equations Using Inverse Operations. [latex]7y[/latex] is the side containing only a variable. Solution: Every day at wikiHow, we work hard to give you access to instructions and information that will help you live a better life, whether it's keeping you safer, healthier, or improving your well-being. Examples are … [latex]2a\color{red}{-2a}-7=5a\color{red}{-2a}+8[/latex]. [latex]-x+24[/latex] is the side containing a constant. [latex]6(\color{red}{1})-2\stackrel{\text{?}}{=}-3(\color{red}{1})+7[/latex].

Subtract [latex]2a[/latex] from both sides to remove the variable term from the left. Boost your career: Improve your Zoom skills. }}{=}15[/latex], [latex]5x[/latex] is the side containing only a. The equations we solved in the last section simplified nicely so that we could use the division property to isolate the variable and solve the equation. }}{=}28+7[/latex], [latex]7x[/latex] is the side containing only a. It makes sense to call the left side the variable side.

Solve a Linear Equation in One Variable with Variables on Both Sides: 2m-9=6m-17. Try these problems to see how well you understand how to solve linear equations with variables and constants on both sides of the equal sign. All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. [latex]4x+6\color{red}{-6}=-14\color{red}{-6}[/latex]. We don’t want any constants on the left side, so add [latex]2[/latex] to both sides. Remove the [latex]-x[/latex] from the right side by adding [latex]x[/latex] to both sides. Therefore, the right side will be the constant side. Either answer works. Perform the multiplications, so that 64 = y², and y = +/- 8. You will see that it doesn’t matter which side you choose to be the variable side; you can get the correct answer either way. We must “undo” adding [latex]6[/latex] by subtracting [latex]6[/latex], and to keep the equality we must subtract [latex]6[/latex] from both sides. Solving Equations with One Variable on Both Sides Apply the distributive property, if necessary. We have solved the equation. BYJU’S online calculator tool makes calculations faster and easier. In the next example, the variable, [latex]x[/latex], is on both sides, but the constants appear only on the right side, so we’ll make the right side the “constant” side. Thus, (2/y)(32y) = (y/32)(32y). How do I solve 3y + 9 = 9x -18? Let’s leave the constant on the left and collect the variables to the right. Divide both sides by [latex]2[/latex]. [latex]x+5\color{red}{-5}=2\color{red}{-5}[/latex], [latex]7(\color{red}{-3})+5\stackrel{\text{?

All the variables are on the left and the constants are on the right. 15 + 0x = 5x The only constant, [latex]24[/latex], is on the right, so let the left side be the variable side. The variable term is on the left and the constant term is on the right. Move the constants to one side by subtracting 36 from each side: Cancel the coefficient by dividing each side by 3. Divide both sides by [latex]3[/latex] to make 1[/latex] the coefficient of [latex]a[/latex] . }}{=}4(\color{red}{7})+7[/latex], [latex]35\stackrel{\text{? If solving for x, divide both sides of the equation by 9. [latex]\frac{9n}{\color{red}{9}}=\frac{9}{\color{red}{9}}[/latex]. It is subtracted from the [latex]2y[/latex], so to “undo” subtraction, add [latex]7[/latex] to both sides. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. Now you solve for one of the variables in terms of the other variable. Choose one side to be the variable side and then the other will be the constant side. That gives you (y/3) + 1 = x - 2. After simplifying, the first step in solving an equation with a variable on both sides is to get the variable on one side. A quantity with a variable can be treated just like a quantity without variables -- a quantity with a variable follows all the rules learned in the last two sections. The only constant, [latex]-8[/latex], is on the left side of the equation, and the variable, [latex]y[/latex], is on both sides. Your ultimate goal is to get all of the constants on one side of the equation and all of the variables on the other side of the equation. Divide both sides by [latex]8[/latex].

}}{=}-(\color{red}{3})+24[/latex], [latex]5y-8[/latex] is the side containing a. Subtract [latex]5y[/latex] from both sides. Include your email address to get a message when this question is answered. Sometimes, after you simplify you may have a variable and a constant term on the same side of the equal sign. [latex]\frac{4x}{\color{red}{4}}=\frac{-20}{\color{red}{4}}[/latex], [latex]2y-7[/latex] is the side containing a, [latex]2y-7\color{red}{+7}=15\color{red}{+7}[/latex]. % of people told us that this article helped them.

The most important thing to remember when solving such equations is that whatever you do to one side of the equation, you must do to the other side.

There is no “correct” side to move the variable term, but the choice can help you avoid working with negative signs. Simplify further by dividing both sides of the equation by 6: 5y = 4x. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. Read on to find out how to solve this kind of equation. Now, collect the constants to the right side by subtracting [latex]5[/latex] from both sides. If you have any fractions, get rid of those first by multiplying ALL terms by the denominator. Solving Equations with One Variable on Both Sides, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/d3\/Solve-Equations-with-Variables-on-Both-Sides-Step-1-Version-2.jpg\/v4-460px-Solve-Equations-with-Variables-on-Both-Sides-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/d\/d3\/Solve-Equations-with-Variables-on-Both-Sides-Step-1-Version-2.jpg\/aid2880110-v4-728px-Solve-Equations-with-Variables-on-Both-Sides-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"