Question

Solve the inequality |x+3| - 2>9

Answer 1

x > 8 ∪ x < -14

Explanation:

Start by adding 2 to both sides, obtaining the simpler inequality

|x+3| >11

Rewriting this as | x -(-3) | >11 makes the solution easier to visualize. Think of (or draw) a number line with an open circle at x = -3. This is the "center."

| x -(-3) | >11 tells us that x is either 11 units greater than -3 or 11 units smaller than -3:

x > 8 ∪ x < -14

Answer 2

x < - 14 or x > 8

Explanation:

|x+3| - 2 > 9

First add two to both sides

That's

| x + 3 | - 2 + 2 > 9 + 2

Simplify

We have

| x + 3 | > 11

Apply the absolute rule

That's

If | u| > a where a > 0 then

u < - a or u > a

So we have

x + 3 < - 11 or x + 3 > 11

For x + 3 < - 11

x + 3 < - 11

x < - 11 - 3

x < - 14

For x + 3 > 11

x + 3 > 11

x > 11 - 3

x > 8

Combine the intervals

We have the final answer as

x < - 14 or x > 8

Hope this helps you