Question

Which set expresses the solution to the compound inequality −2 ≤ (2x+1)/3 −4 < 1

Answer 1

To solve the compound inequality −2 ≤ (2x+1)/3 − 4 < 1, let's first isolate the terms involving x. We'll do this by first getting rid of the -4 and the division by 3.

Starting with −2 ≤ (2x+1)/3 − 4, we add 4 to all three parts of the inequality:

−2 + 4 ≤ [(2x+1)/3 − 4] + 4 < 1 + 4

2 ≤ (2x+1)/3 < 5

Now, to get rid of the division by 3, we'll multiply all parts by 3:

3 * 2 ≤ 3 * (2x+1)/3 < 3 * 5

6 ≤ 2x + 1 < 15

Next, subtract 1 from all three parts to isolate the term with x:

6 − 1 ≤ 2x + 1 − 1 < 15 − 1

5 ≤ 2x < 14

Finally, divide all parts by 2 to solve for x:

5/2 ≤ x < 14/2

2.5 ≤ x < 7

The solution set to the compound inequality is the interval [2.5, 7), meaning x is greater than or equal to 2.5 and less than 7.