−22 > −5x − 7 ≥ −3 is our compound equality and we want to find an equivalent form. You can break this into separate inequalities with "OR" in between, or, treat it as one.
−22 > −5x − 7 ≥ −3
-22 > -5x - 7 OR -5x - 7 ≥ -3 <-----pull apart into two separate inequalities
-15 > -5x <-------------------------------add 7 to both sides
15 < 5x <-------------------------------multiply by -1 to change orientation
3 < x <-------------------------------divide both sides by 5
-5x - 7 ≥ -3 <-----------------------------Now work with the second inequality
-5x ≥ 4 <-----------------------------add 7 to both sides
5x ≤ -4 <-----------------------------multiply both sides by -1 to change orientation
x ≤ -4/5 <-----------------------------divide both sides by 4
3 < x or x ≤ -4/5 <-----------------------put the two inequalities together
Thus x ≤ -4/5 or x > 3 is an equivalent form.
