Question

solve for d.
5|6d| ≤ 75
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. u fractions, or improper fractions in simplest form.

Explanation:

Step1: Divide both sides by 5

To isolate the absolute value expression, we divide both sides of the inequality \(5|6d| \leq 75\) by 5.
\(\frac{5|6d|}{5} \leq \frac{75}{5}\)
Simplifying, we get \(|6d| \leq 15\)

Step2: Solve the absolute value inequality

The absolute value inequality \(|6d| \leq 15\) is equivalent to the compound inequality \(-15 \leq 6d \leq 15\) because if \(|x| \leq a\) (where \(a \geq 0\)), then \(-a \leq x \leq a\).

Step3: Divide all parts by 6

To solve for \(d\), we divide each part of the compound inequality \(-15 \leq 6d \leq 15\) by 6.
\(\frac{-15}{6} \leq \frac{6d}{6} \leq \frac{15}{6}\)
Simplifying the fractions, we have \(-\frac{5}{2} \leq d \leq \frac{5}{2}\)

Answer:

\(-\frac{5}{2} \leq d \leq \frac{5}{2}\)