Solve Linear Equations With Variables On Both Sides Worksheet

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Solving linear equations with variables on both sides means to find the solution of a linear equation having variables on both the sides. Solving such equations requires rearranging the terms and applying different mathematical operations to isolate the variable alone on one side and making sure that the equation stays balanced. The main aim is to find the value of the variable that makes the equation true. In these worksheets, students will isolate the variable term by applying different arithmetic operations.

For example: Solve for $ r $: $-10 - 5r = -6r - 1$

Algebra 1

One-Variable Equations

How Will This Worksheet on "Solve Linear Equations with Variables on Both Sides" Benefit Your Students' Learning?

It helps to understand the concept of maintaining equality by performing the same operations on both sides of the equation.
It fosters logical thinking and enhances the ability to tackle complex problems.
It helps to practice different algebraic techniques such as combining like terms, dis...

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Solved Example

Q. Solve for

u

\newline

9 + 5u = 7u - 9

\newline

u = \_\_\_

Solution:

Start Equation Isolation: Start with the equation $9 + 5u = 7u - 9$ . To isolate the variable $u$ , we need to get all the $u$ terms on one side and the constant terms on the other side.
Subtract $5u$ : Subtract $5u$ from both sides to move the u terms to one side. $\newline$ $9 + 5u - 5u = 7u - 9 - 5u$ $\newline$ This simplifies to: $\newline$ $9 = 2u - 9$
Add $9$ : Add $9$ to both sides to move the constants to the other side. $\newline$ $9 + 9 = 2u - 9 + 9$ $\newline$ This simplifies to: $\newline$ $18 = 2u$
Divide by $2$ : Divide both sides by $2$ to solve for $u$ . $\newline$ $\frac{18}{2} = \frac{2u}{2}$ $\newline$ This simplifies to: $u = 9$