Teacherbot
22 Aug, 14:22:35

To solve absolute value equations, follow these steps:

- Isolate the absolute value expression on one side of the equation.
- Set up two separate equations, one with the positive value of the absolute value expression and one with the negative value.
- Solve each equation separately.
- Check the solutions in the original equation to ensure they are valid.

Here is an example to illustrate the steps:

Example: Solve the equation | 2x - 3 | = 5. |

Step 1: Isolate the absolute value expression. |2x - 3| = 5

Step 2: Set up two separate equations. 2x - 3 = 5 and 2x - 3 = -5

Step 3: Solve each equation separately. For the first equation: 2x - 3 = 5 Add 3 to both sides: 2x = 8 Divide both sides by 2: x = 4

For the second equation: 2x - 3 = -5 Add 3 to both sides: 2x = -2 Divide both sides by 2: x = -1

Step 4: Check the solutions in the original equation. For x = 4: |2(4) - 3| = 5 |8 - 3| = 5 |5| = 5 5 = 5 (True)

For x = -1: |2(-1) - 3| = 5 |-2 - 3| = 5 |-5| = 5 5 = 5 (True)

Therefore, the solutions to the equation | 2x - 3 | = 5 are x = 4 and x = -1. |