Questions: Solve the inequality for (w). [ -8<-4 w+4 ] Simplify your answer as much as possible.

Solution Steps

To solve the inequality \(-8 < -4w + 4\), we need to isolate the variable \(w\). Start by subtracting 4 from both sides to eliminate the constant term on the right. Then, divide both sides by -4, remembering to reverse the inequality sign because we are dividing by a negative number.

Start with the given inequality: \[ -8 < -4w + 4 \] Subtract 4 from both sides to isolate the term with \(w\): \[ -8 - 4 < -4w \] This simplifies to: \[ -12 < -4w \]

Divide both sides by \(-4\) to solve for \(w\). Remember to reverse the inequality sign because we are dividing by a negative number: \[ \frac{-12}{-4} > w \] This simplifies to: \[ 3 > w \] or equivalently: \[ w < 3 \]

Final Answer