Algebra-1

To solve the inequality 3 |2x + 7| - 7 < -4, we can begin by adding 7 to both sides:

3 |2x + 7| < 3

Next, we can divide both sides of the inequality by 3:

|2x + 7| < 1

Now, we can break it down into two cases:

Case 1: 2x + 7 is nonnegative (i.e., 2x + 7 ≥ 0)
In this case, the absolute value |2x + 7| is equal to 2x + 7, so we have:
2x + 7 < 1

Solving this inequality, we get:
2x < 1 - 7
2x < -6

Dividing both sides of the inequality by 2, we have:
x < -3

Case 2: 2x + 7 is negative (i.e., 2x + 7 < 0)
In this case, the absolute value |2x + 7| is equal to -(2x + 7), so we have:
-(2x + 7) < 1

Simplifying this inequality, we get:
-2x - 7 < 1

Adding 7 to both sides of the inequality, we have:
-2x < 1 + 7
-2x < 8

Dividing both sides of the inequality by -2 reverses the inequality sign:
x > -4

So the solution to the inequality 3 |2x + 7| - 7 < -4 is:
x < -3 and x > -4

Comparing the solution to the given answer choices:

A. x < -3 and x >

Click "Show Answer" to reveal the answer and analysis