Question

this is another way to express an and compound inequality.

12 ≤ 2x + 2 ≤ 40

when we write a compound inequality that way, it means:

12 ≤ 2x + 2 and 2x + 2 ≤ 40

this only works for and compound inequalities. there are no different ways to express an or compound inequality, except to put the word or in between the two inequalities.

solve the above and compound inequality and select the correct solution from the choices below:

○ 5 ≤ x ≤ 19 (...which means x ≥ 5 and x ≤ 19)
○ 6 ≤ x ≤ 20 (...which means x ≥ 6 and x ≤ 20)
○ 10 ≤ x ≤ 38 (...which means x≥6 and x≤20)

Explanation:

Step1: Subtract 2 from all parts

To solve the compound inequality \(12 \leq 2x + 2 \leq 40\), we first subtract 2 from each part of the inequality. This gives us \(12 - 2 \leq 2x + 2 - 2 \leq 40 - 2\), which simplifies to \(10 \leq 2x \leq 38\).

Step2: Divide all parts by 2

Next, we divide each part of the inequality \(10 \leq 2x \leq 38\) by 2. This results in \(\frac{10}{2} \leq \frac{2x}{2} \leq \frac{38}{2}\), which simplifies to \(5 \leq x \leq 19\).

Answer:

\(5 \leq x \leq 19\) (…which means \(x \geq 5\) AND \(x \leq 19\))