Question: what is the absolute value inequalities of -3 -4|-2x -5|≥-7 ?
The inequality is:
-3 -4|-2x -5|≥-7 -- add 3 to both sides
-4|-2x -5|≥ - 4 -- divide both sides by 4
-|-2x - 5|≥ - 1 -- change sign and adjust inequality
|-2x - 5| ≤ 1
In effect, we have two inequalitie, viz.
(-2x - 5) ≤ 1 and -(-2x - 5) ≤ 1
1st inequality
(-2x - 5) ≤ 1 -- add 5 to both sides
-2x ≤ 6 ------- divide both sides by 2
-x ≤ 3 ------ adjust sign and inequality
x ≥ - 3
2nd inequality
-(-2x - 5) ≤ 1 -- expand bracket
2x + 5 ≤ 1 -- subtract 5 from both sides
2x ≤ -4 ------ divide both sides by 2
x ≤ -2
Our two inequalities then are: x ≥ - 3 and x ≤ -2, which combine to give -3 ≤ x ≤ -2