Question

solve the compound inequality.
3.9 < 0.7x - 0.3 < 10.2
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is ∅.

Explanation:

Step1: Add 0.3 to all parts

To isolate the term with \(x\), we add \(0.3\) to each part of the compound inequality \(3.9 < 0.7x - 0.3 < 10.2\). This gives us \(3.9 + 0.3 < 0.7x - 0.3 + 0.3 < 10.2 + 0.3\), which simplifies to \(4.2 < 0.7x < 10.5\).

Step2: Divide all parts by 0.7

To solve for \(x\), we divide each part of the inequality \(4.2 < 0.7x < 10.5\) by \(0.7\). Calculating each division: \(\frac{4.2}{0.7}=6\) and \(\frac{10.5}{0.7}=15\). So we get \(6 < x < 15\).

Step3: Write in interval notation

The solution \(6 < x < 15\) in interval notation is \((6, 15)\).

Answer:

A. The solution set is \((6, 15)\)