Question

Solve for xx and graph the solution on the number line below.
minus, x, minus, 5, is greater than or equal to, 1, or, minus, x, minus, 5, is less than, minus, 8
−x−5≥1or
−x−5<−8

Answer 1

Solve each part separately.

1) −x − 5 ≥ 1
Add 5: −x ≥ 6
Multiply by −1 (reverse inequality): x ≤ −6

2) −x − 5 < −8
Add 5: −x < −3
Multiply by −1 (reverse inequality): x > 3

Solution: x ≤ −6 or x > 3. Interval notation: (−∞, −6] ∪ (3, ∞).

Number line (● = included, ○ = not included):

...——●================ ○——...
-∞ -6 0 3 ∞

(Left ray filled at −6; right ray starts open at 3.)