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

Solution:

The inequality representing the given compound inequality can be derived as follows:

Proceeding with LHS of the compound inequality we obtain:

-22 > - 5x - 7

After changing the inequality sign the resulting equation is:

5x + 7 > 22

5x > 22 - 7

5x > 15

x > 3 --- (1)

Proceeding with RHS of the compound inequality we obtain:

- 5x - 7 ≥ 3

5x + 7 ≤ - 3

5x ≤ -10

x ≤ -2 --- (2)

Both (1) and (2) can be represented on the number line as the solution to this problem.

The inequality representing the given compound inequality is represented on the number line as the solution to the problem.

Please note the dot symbols on the number line to represent x ≤ -2 and x > 3. The “ ≤ “ inequality shows a red dot on the number at x = -2 while the “>” inequality is represented by an arrow with a blue dot at x = 3. The point x = -2 is included along with the area on the left of the point while x=3 is not included with the area to the right of the point.

Therefore, the solution to the compound inequality -22 > -5x - 7 ≥ -3 is given as 3 < x ≤ -2

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

Summary:

An equivalent form of the compound inequality -22 > -5x - 7 ≥ -3 is given as 3 < x ≤ -2