Solving Equations with the Variable on Both Sides

In this lesson, we will look into solving equations that have a term with the variable on both sides of the equation.

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.

Example:

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)

Step 2: Combine like terms

2x + x = 3 + 6

3x = 9

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

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.

Example:

Solve 6x – 4 = 3x + 2

Solution:

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)

Step 2: Combine like terms

6x – 3x = 2 + 4

3x = 6

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

Videos

The following video shows more examples of solving equations with variables on both sides.

Solving Equations with Variables on Both Sides .

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