Question

solve the inequality for y.
-7y + 4(y - 2) > -23
simplify your answer as much as possible.

Explanation:

Step1: Expand the bracket

First, we expand the term \(4(y - 2)\) using the distributive property \(a(b - c)=ab - ac\). So we have:
\(-7y+4y - 8>-23\)

Step2: Combine like terms

Combine the \(y\)-terms \(-7y\) and \(4y\). \(-7y + 4y=-3y\), so the inequality becomes:
\(-3y-8 > - 23\)

Step3: Add 8 to both sides

To isolate the term with \(y\), we add 8 to both sides of the inequality. Adding 8 to both sides gives:
\(-3y-8 + 8>-23 + 8\)
Simplifying both sides, we get \(-3y>-15\)

Step4: Divide by - 3 (and reverse inequality)

When we divide both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. Dividing both sides of \(-3y>-15\) by \(-3\) gives:
\(y < 5\)

Answer:

\(y < 5\)