Question

Which of the following is an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8?

Answer 1

To find an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8, we simplify each inequality separately. The equivalent form is 18 < x ≤ 0.

Step-by-step explanation:

To find an equivalent form of the compound inequality −44 > −2x − 8 ≥ −8, we can start by simplifying each inequality separately.

For the first inequality, we add 8 to both sides to isolate the variable:

-44 + 8 > -2x - 8 + 8

-36 > -2x

Then we divide by -2 to solve for x, remembering to reverse the inequality sign:

-36/-2 < -2x/-2

18 < x

For the second inequality, we add 8 to both sides:

-2x - 8 + 8 ≥ -8 + 8

-2x ≥ 0

Then we divide by -2, remembering to reverse the inequality sign:

-2x/-2 ≤ 0/-2

x ≤ 0

So the equivalent form of the compound inequality −44 > −2x − 8 ≥ −8 is 18 < x ≤ 0.

Answer 2

0 ≤ x < 18

Step-by-step explanation:

We will go step by step, first subtract 8 from the expression

1. −44 > −2x − 8 ≥ −8
2. -36 > -2x ≥ 0 now divide it by 2
3. -18 > -x ≥ 0 and multply by -1 so we can have x not -x
4. 0 ≤ x < 18 this is the final result