Question

Solve the following and type all the steps you did: 4|x - 5| + 20 = 60

Answer 1

To solve the equation 4|x - 5| + 20 = 60, subtract 20, divide by 4, and consider both positive and negative cases of the absolute value, resulting in the solutions x = 15 and x = -5.

Step-by-step explanation:

To solve the equation 4|x - 5| + 20 = 60, follow these steps:

1. Subtract 20 from both sides of the equation to isolate the absolute value expression: 4|x - 5| = 40.
2. Divide both sides by 4 to further isolate the absolute value: |x - 5| = 10.
3. Now, consider the two possible cases for the absolute value:

• Case 1: x - 5 = 10, which simplifies to x = 15.
• Case 2: x - 5 = -10, which simplifies to x = -5.

Therefore, the solutions to the equation are x = 15 and x = -5.