Which of the following describes all solutions of the compound inequality - 10 <= 2x - 6 <= 4 ?

Rationale

-2 ≤ x ≤ 5

To solve the compound inequality -10 ≤ 2x - 6 ≤ 4, break it into two parts:
2x - 6 ≥ -10 and 2x - 6 ≤ 4.

Add 6 to each part:
2x ≥ -4 and 2x ≤ 10.

Divide by 2:
x ≥ -2 and x ≤ 5.

So, the solution is the inclusive interval -2 ≤ x ≤ 5.

A (x <= - 2 or x >= 5) YOUR ANSWER

This option suggests values outside the interval between -2 and 5. However, the inequality requires x to be between these two values, not outside them. Therefore, this is incorrect.

B (-4 <= x <= 10) YOUR ANSWER

This option comes from stopping too early in the solving process (before dividing by 2). Since we must divide all parts of the inequality by 2, this interval is too wide and does not represent the correct solution.

C (-2 < x < 5) YOUR ANSWER

This option excludes the endpoints -2 and 5. However, the original inequality uses “≤”, meaning the endpoints are included. So this answer is close but still incorrect.

D (-2 <= x <= 5) CORRECT

This correctly represents the solution. It includes all values between -2 and 5, including both endpoints, matching the result of solving the compound inequality.

E (x >= -2) YOUR ANSWER

This only satisfies one side of the inequality and ignores the upper bound (x ≤ 5). Since both conditions must be true at the same time, this option is incomplete and incorrect.

Conclusion

The solution to the compound inequality is -2 ≤ x ≤ 5. Option D is correct because it accurately represents all values that satisfy both parts of the inequality, while the other options either exclude valid values, include invalid ones, or fail to represent the full solution set.

Which of the following describes all solutions of the compound inequality - 10 <= 2x - 6 <= 4 ?

-2 ≤ x ≤ 5

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