Question

Solve the following inequality. Write the answer in interval notation.
If the answer includes more than one interval write the intervals separated by the "union" symbol, U.

Answer 1

\[\left| x+2 \right|\ge7\]

Answer 2

After working the problem out I received [-9,-5] where did I go wrong? @Hero

Answer 3

While no one is looking, re-write it in this manner

-7 ≥ x+2 ≥ 7 (so that you know where the symbols should point, but not a valid step)

Then afterwards, split into two equations

x + 2 ≥ 7
x + 2 ≤ -7

Then solve each equation for x

x ≥ 7 - 2
x ≤ -7 - 2

x ≥ 5
x ≤ - 9

So it should be

[-∞, -9] U [5, ∞]

Answer 4

What makes our answers different?

Answer 5

Come to think about it @Hero shouldn't it be (-infinity,-9]U[5,infinity)

Answer 6

Yes, I goof up on that notation sometimes.

Answer 7

Its Okay.