Solving Difficult Equations Help

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

Solving More Difficult Equations

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Solving More Difficult Equations

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

Example 2

Solve 3(2x + 6) = 30.

Solution 2

Solving More Difficult Equations

Check:

Solving More Difficult Equations

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

Solving More Difficult Equations

Check:

Solving More Difficult Equations

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.

Solving Difficult Equations Help