Express the set − 2 x + 30 ≤ 4 x + 12 using interval notation.

Answer 1

-2x + 30 ≤ 4x + 12

Let's simplify and solve for x.

1) Flip to put 4x +12 ≥on left, but change inequality sign.

4x + 12 ≥ -2x + 30

2) Add 2x to both sides.

4x + 12 + 2x ≥ -2x + 30 + 2x

6x + 12 ≥ 30

3) Subtract 12 from both sides.

6x + 12 - 12 ≥ 30 - 12

6x ≥ 18

4) Divide both sides by 6.

6x/6 ≥ 18/6

x ≥ 3

5) Interval notation:

x ≥ 3 or [3, ∞)

NOTE: Always put a parentheses ')' after infinity since you can never get there.

Answer 2

 − 2 x + 30 ≤ 4 x + 12

18≤6x

3≤x