Algebra-1

Apologies for the previous incorrect response. Let's solve the inequality again:

Given inequality: |5x + 7| < 22

We'll break it down into two cases:

Case 1: 5x + 7 is nonnegative (i.e., 5x + 7 ≥ 0)
In this case, the absolute value |5x + 7| is equal to 5x + 7, so we have:
5x + 7 < 22

Solving this inequality, we get:
5x < 22 - 7
5x < 15
x < 3

Case 2: 5x + 7 is negative (i.e., 5x + 7 < 0)
In this case, the absolute value |5x + 7| is equal to -(5x + 7), so we have:
-(5x + 7) < 22

Multiplying both sides of the inequality by -1, we change the direction of the inequality:
5x + 7 > -22

Solving this inequality, we get:
5x > -22 - 7
5x > -29
x >

So the solution to the inequality |5x + 7| < 22 is:

Click "Show Answer" to reveal the answer and analysis