What are the solutions for x in the equation |(2/5)x - 1| = 7?

To solve the equation |(2/5)x - 1| = 7, we need to consider the definition of absolute value. The equation states that the expression within the absolute value can equal either 7 or -7. This gives us two separate equations to solve:

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

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

Let's solve each equation step-by-step.

For the first equation, we can isolate x:

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

Adding 1 to both sides gives (2/5)x = 8.

To eliminate the fraction, we multiply both sides by 5:

2x = 40.

Dividing both sides by 2 results in x = 20.

Next, we solve the second equation:

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

Adding 1 to both sides gives (2/5)x = -6.

Again, we multiply both sides by 5 to eliminate the fraction:

2x = -30.

Dividing by 2 results in x = -15.

Thus, the solutions for