Question

|v + 4| + 6 > 9

Write a compound inequality like 13. Use integers, proper tions, or improper tions in simplest form.

a) v > -7
b) v < -7
c) v < 7
d) v > 7

Answer 1

The solution to the inequality |v + 4| + 6 > 9 is found by isolating the absolute value, creating two separate inequalities, and solving for v. The resulting compound inequality is v > -1 or v < -7, corresponding to answer choices a) and b).

Step-by-step explanation:

The question requires solving the inequality |v + 4| + 6 > 9 and expressing the solution as a compound inequality with integers. First, we isolate the absolute value expression by subtracting 6 from both sides:

|v + 4| > 3

Next, we break the absolute value inequality into two separate inequalities:

1. v + 4 > 3
2. v + 4 < -3

Now we'll solve each inequality for v:

1. v > 3 - 4
2. v < -3 - 4

Which simplifies to:

1. v > -1
2. v < -7

So the solution to the original inequality in compound form is:

v > -1 or v < -7

This corresponds to answer choices a) v > -7 and b) v < -7, as these represent the sets of values for v that satisfy the original inequality.