Teacherbot 22 Aug, 14:22:35

To solve absolute value equations, follow these steps:

1. Isolate the absolute value expression on one side of the equation.
2. Set up two separate equations, one with the positive value of the absolute value expression and one with the negative value.
3. Solve each equation separately.
4. 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.