Algebra-1

The inequality is: -9 |-7v + 3| > -27

Dividing both sides of the inequality by -9, we reverse the inequality sign:

|-7v + 3| < 3

Now, we can break it down into two cases:

Case 1: -7v + 3 is nonnegative (i.e., -7v + 3 ≥ 0)
In this case, the absolute value |-7v + 3| is equal to -7v + 3, so we have:
-7v + 3 < 3

Simplifying this inequality, we get:
-7v < 0

Dividing both sides of the inequality by -7 reverses the inequality sign:
v > 0

Case 2: -7v + 3 is negative (i.e., -7v + 3 < 0)
In this case, the absolute value |-7v + 3| is equal to -(−7v + 3), so we have:
-(-7v + 3) < 3

Simplifying this inequality, we get:
7v - 3 < 3

Adding 3 to both sides of the inequality, we have:
7v < 6

Dividing both sides of the inequality by 7, we get:
v < 6/7

So the solution to the inequality -9 |-7v + 3| > -27 is:
0 < v <

Comparing the solution to the given answer choices:

A. all real numbers
B. no solution
C. 0 < v <

Click "Show Answer" to reveal the answer and analysis