In these lessons, we will learn to solve equations that have a term with the variable on both sides of the equation.

**Related Pages**

Solving Equations

Basic Algebra

Combining Like Terms

Algebra - Transposition

More Algebra Lessons

The following figure shows how to solve equations with variables on both sides. Scroll down the page for more examples and solutions.

**Example:**

Consider the equation x – 6 = –2x + 3.

To isolate the variable, we need to get all the variable terms to one side and the constant terms
to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.

Solve x – 6 = –2x + 3

**Solution:**

Step 1: Get all the variable terms to one side and the constant
terms to the other side.

x – 6 = –2x + 3

x – 6 + 2x + 6 = –2x + 3 + 2x + 6 (Add 2x & 6 to
both sides)

<span class=“highlight-step>Step 2: Combine like terms

2x + x = 3 + 6

3x = 9

<span class=“highlight-step>Step 3: Divide or multiply to isolate the variable

3x = 9 (Divide by 3)

x = 3

**Check:**

x – 6 = –2x + 3

3 – 6 = –2 • 3 + 3 (substitute x = 3 into
the original equation)

–3 = –3

**Example:**

Consider the equation 6x – 4 = 3x + 2. To isolate the variable, we need to get all the
variable terms to one side and the constant terms to the other side. Next, we combine like
terms and then isolate the variable by multiplying or dividing.

Solve 6x – 4 = 3x + 2

**Solution:**

<span class=“highlight-step>Step 1: Get all the variable terms to one side and the constant
terms to the other side.

6x – 4 = 3x + 2

6x – 4 – 3x + 4 = 3x + 2 – 3x + 4 (Subtract 3x &
add 4 to both sides)

<span class=“highlight-step>Step 2: Combine like terms

6x – 3x = 2 + 4

3x = 6

<span class=“highlight-step>Step 3: Divide or multiply to isolate the variable

3x = 6 (Divide by 3)

x = 2

**Check:**

6x – 4 = 3x + 2 (substitute x = 2 into the original equation)

6 • 2 – 4 = 3 • 2 + 2

8 = 8

**How to solve equations with variables on both sides of the equation?**

Examples:

- 5x + 8 = 7x
- 4w + 8 = 6w – 4
- 6(g + 3) = – 2(g + 31)

**Solving Equations with Variables on Both Sides**

Step 1: Add and subtract terms to get the variables on one side and the constants on the other.

Step 2: Multiply or divide to isolate the variable.

Examples:

- 2x + 7 = 4x – 7
- 3x + 19 = 3 – 5x

**Equations With Variables on Both Sides**

This requested video looks at solving equations with variables on both sides. It includes four examples.

Examples:

- x + 14.8 = 102 – 7x
- 5y – 2 = 28 – y
- 3 + 5m = 8m – 9
- 4 + 3x – 6 = 3x + 2 – x

**How to use the distributive property to simplify equations with variables on both sides?**

Examples:

- 3(x – 1) = 2(x + 3)
- z/6 = 2(z + 1)/9

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