Question

Solve 2x - 7 ≥ 1 ≥ x-10. Write the solution using set-builder notation.

A) 11 ≤ x ≤4
B) {x|4 ≤ x ≤ 111
C) 3 ≤ x ≤ 9
D) x

Answer 1

The solution to the compound inequality 2x - 7 ≥ 1 ≥ x - 10 is x ≥ 4 and x ≤ 11, which in set-builder notation is 4 ≤ x ≤ 11. The correct answer is D) after correcting -4 to 4.

Step-by-step explanation:

To solve the compound inequality 2x - 7 ≥ 1 ≥ x - 10, we'll break it down into two separate inequalities and solve each one individually.

First, for the left part of the inequality 2x - 7 ≥ 1, we add 7 to both sides to get 2x ≥ 8, and then we divide by 2 to find x ≥ 4.

Next, for the right part of the inequality 1 ≥ x - 10, we add 10 to both sides to get 11 ≥ x, which can also be written as x ≤ 11.

Combining both parts of the solution, we get 4 ≤ x ≤ 11. Therefore, the solution in set-builder notation is x .

The correct answer from the provided options is D) -4 ≤ x ≤ 11 with a typo corrected to 4 instead of -4.