Question

solve for y.
-2|y| < -4
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: Divide both sides by -2 (reverse inequality)

When dividing an inequality by a negative number, the inequality sign flips. So, divide both sides of \(-2|y| < -4\) by \(-2\):
\(\frac{-2|y|}{-2} > \frac{-4}{-2}\)
Simplifying gives \(|y| > 2\)

Step2: Solve the absolute value inequality

The absolute value inequality \(|y| > 2\) means that \(y\) is either less than \(-2\) or greater than \(2\). This is because the absolute value of a number represents its distance from zero on the number line, so if the distance is greater than 2, the number is either to the left of \(-2\) or to the right of \(2\) on the number line.

Answer:

\(y < -2\) or \(y > 2\)