Question

consider the following compound inequality.
\\(\frac{20}{4} < \frac{x + 4}{2} < \frac{25}{4}\\)
step 1 of 2: solve the inequality and express your answer in interval notation. use decimal form for numerical values.

Explanation:

Step1: Simplify fractions

Simplify \(\frac{20}{4}\) to \(5\) and \(\frac{25}{4}\) to \(6.25\). The inequality becomes \(5 < \frac{x + 4}{2} < 6.25\).

Step2: Multiply by 2

Multiply all parts of the inequality by \(2\) to eliminate the denominator: \(5\times2 < \frac{x + 4}{2}\times2 < 6.25\times2\), which simplifies to \(10 < x + 4 < 12.5\).

Step3: Subtract 4

Subtract \(4\) from all parts: \(10 - 4 < x + 4 - 4 < 12.5 - 4\), resulting in \(6 < x < 8.5\).

Step4: Write in interval notation

The interval notation for \(6 < x < 8.5\) is \((6, 8.5)\).

Answer:

\((6, 8.5)\)