Question

solve for y.\\
\\
|-2y - 8| < 10\\
\\
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. use inte\\
fractions, or improper fractions in simplest form.

Explanation:

Step1: Apply absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|-2y - 8| < 10\), we get \(-10 < -2y - 8 < 10\).

Step2: Add 8 to all parts

Add 8 to each part of the compound inequality: \(-10 + 8 < -2y - 8 + 8 < 10 + 8\), which simplifies to \(-2 < -2y < 18\).

Step3: Divide by -2 (reverse inequalities)

Divide each part by -2. Remember that when dividing by a negative number, the inequality signs reverse. So \(\frac{-2}{-2} > \frac{-2y}{-2} > \frac{18}{-2}\), which simplifies to \(1 > y > -9\) or rewritten as \(-9 < y < 1\).

Answer:

\(-9 < y < 1\)