**Solving Difficult Equations**

When an equation has like terms on the same side, these terms can be combined first.

**Examples**

**Example 1**

Solve 2x + 5 + 3x = 30.

**Solution 1**

Check:

If an equation has parentheses, use the distributive property to remove parentheses.

**Example 2**

Solve 3(2x + 6) = 30.

**Solution 2**

Check:

**Solving Equations Procedure**

*The procedure for solving equations in general is:*

*Step 1 Remove parentheses*.*Step 2 Combine like terms on each side of the equation*.*Step 3 Use the addition and/or subtraction principle to get the variables on one side and the constant terms on the other side*.*Step 4 Use the division principle to solve for x*.*Step 5 Check the equation*.

**Example 3**

Solve 5(2x – 7) – 3x = 5x + 9.

**Solution 3**

Check:

### Solving Difficult Equations Practice Problems

**Practice**

Solve each of the following equations:

1. 6x + 4 = 2x + 12

2. x – 10 = 32 – 5x

3. 9x – 5 + 2x = 17

4. 7x – 3 = 4x – 27

5. 10x + 36 = 6x

6. 3(x – 2) = 24

7. 4(2x – 5) = 20

8. 8x – 2(3x – 7) = 20

9. 5(x + 6) = 10

10. 9(3x – 1) = 8(3x – 6)

**Answers**

1. 2

2. 7

3. 2

4. –8

5. –9

6. 10

7. 5

8. 3

9. –4

10. –13

Practice problems for this concept can be found at: Expressions And Equations Practice Test.

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