Solving Absolute Value Equations »

Equations with no parentheses

Example 1

Solve 5x - 4 - 2x + 3 = -7 - 3x + 5 + 2x

Solution 1

Step 1: Combine the similar terms
Step 2: Add x to both sides.
Step 3: Add 1 to both sides.
Step 4: Divide both sides by 2:
Solution is:

Exercise 1: Solve equations

Equations with parentheses

Example 2

Solve

Solution 2

Step 1: Simplify both sides:
Step 2: Subtract x from both sides.
Step 3: Divide both sides by -3:
Solution is:

Exercise 2: Solve equations

Equations containing fractions

Example 3

Solve

Solution 3

Step 1: Multiply both sides by the LCD. Lowest common multiple of 2 and 3 is 6. So, we multiply both sides by 6.
Step 2: Remove brackets:
Step3: This problem is similar the previous
Solution is:

Exercise 3: Solve equations

More Complicated Example

Example 4

Solution 4

In this case the LCD is (x + 2)(x - 10). Here is the complete solution to this problem.

Much more Complicated Example

Example 5

Solution 4

The first step is to factor the denominators

The LCD is (x + 3)(x + 2). The solution is:

Exercise 4: Solve equations