Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?

−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.

take it another