Solve:
| 0.5x – 1 | =< | x + 2 |
x = -6 and x = -2/3
For this to be true, x is of any value between x = -6 and x = -2/3. I’ve also included my range to x values greater than x = -2/3.
In essence, any value from -6 and greater makes the inequality true.
However, I was marked wrong. What am I missing?
✅ Answers
? Best Answer
=>
0.5x – 1 ≤ | x + 2 |
and
-| x + 2 | ≤ 0.5x – 1
=>
0.5x – 1 ≤ x + 2 or x + 2 ≤ 1 – 0.5x
and
1 – 0.5x ≤ x + 2 or x + 2 ≤ 0.5x – 1
=>
-6 ≤ x or x ≤ -2/3 (satisfied by every x)
and
-2/3 ≤ x or x ≤ -6
=>
x ∈ (-∞,-6]∪[-2/3,∞)
See plot:
http://www.wolframalpha.com/input/?i=plo…