Question

Solve the absolule value equation. |(2x-7)/(3)|=5

Answer 1

The absolute value equation |(2x-7)/3|=5 yields two solutions: x = 11 and x = -4, after separating the equation into its positive and negative counterparts.

Step-by-step explanation:

To solve the absolute value equation |(2x-7)/3|=5, we can split it into two separate equations based on the definition of absolute value:

1. (2x - 7)/3 = 5
2. (2x - 7)/3 = -5

Solving the first equation:

• 2x - 7 = 15
• 2x = 22
• x = 11

Solving the second equation:

• 2x - 7 = -15
• 2x = -8
• x = -4

Thus, the solution to the equation are x = 11 and x = -4.