Question

Graph the solution to the inequality on the number line.

|v+6| >. 2
-
v+6>2 V+6<-2

Answer 1

To graph the inequality |v+6| > 2, we solve for v in the two inequalities v + 6 > 2 and v + 6 < -2, leading to v > -4 and v < -8.

Step-by-step explanation:

We need to graph the solution to the inequality |v+6| > 2. This means we are looking for the values of 'v' where the absolute value of 'v+6' is greater than 2. We handle the absolute value inequality by breaking it into two separate inequalities. The first is v + 6 > 2, and the second is v + 6 < -2.

For the first inequality, we subtract 6 from both sides to get v > -4. Graphically, this means we shade to the right of -4 on the number line.

For the second inequality, we also subtract 6 from both sides to get v < -8. Graphically, this means we shade to the left of -8 on the number line.

The solution to the original inequality consists of the combined shaded areas from both inequalities, thereby showing all the values of 'v' that satisfy the original inequality.We graph the solutions on the number line, shading to the right of -4 and to the left of -8, showing the ranges that satisfy the original inequality.