How to Solve an Equation with Variables on Both Sides

Step-by-step solution

1. Subtract 3x from both sides.

   $$5x - 4 - 3x = 3x + 8 - 3x$$

   Why: Subtracting the same term from both sides keeps the equation balanced.

2. Combine like terms.

   $$2x - 4 = 8$$

   Why: 5x minus 3x is 2x, and 3x minus 3x is 0.

3. Add 4 to both sides.

   $$2x - 4 + 4 = 8 + 4$$

   Why: Adding undoes the subtraction on the left side.

4. Divide both sides by 2.

   $$\frac{2x}{2} = \frac{12}{2}$$

   Why: Dividing by the coefficient leaves x alone.

5. Write the answer and check it.

   $$x = 6$$

   Why: 5(6) - 4 = 26 and 3(6) + 8 = 26, so both sides match.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $4x + 3 = 2x + 9$

   Show answer

   $x = 3$

2. 2

   $6x - 5 = 3x + 7$

   Show answer

   $x = 4$

3. 3

   $7x + 2 = 5x + 10$

   Show answer

   $x = 4$

4. 4

   $2x - 8 = x + 1$

   Show answer

   $x = 9$

5. 5

   $9x - 3 = 4x + 12$

   Show answer

   $x = 3$