Algebra-1

To solve the inequality −5|x − 4| > −20, we can begin by dividing both sides of the inequality by -5. However, we need to be careful about the direction of the inequality when dividing by a negative number. Dividing both sides by -5 reverses the inequality sign, which gives us:

|x - 4| < 4

Now, we can break it down into two cases:

Case 1: x - 4 is nonnegative (i.e., x - 4 ≥ 0)
In this case, the absolute value |x - 4| is equal to x - 4, so we have:
x - 4 < 4

Solving this inequality, we get:
x < 4 + 4
x < 8

Case 2: x - 4 is negative (i.e., x - 4 < 0)