Question

Faith wants to know which inequality is equivalent to the following: -2(w-4)≧12

Answer 1

To solve the inequality \(-2(w - 4) \geq 12\), we can start by distributing the \(-2\) on the left side:

\[
-2w + 8 \geq 12
\]

Next, we subtract 8 from both sides:

\[
-2w \geq 12 - 8
\]

This simplifies to:

\[
-2w \geq 4
\]

Now, we divide both sides by \(-2\). Remember that when dividing by a negative number, we need to reverse the inequality sign:

\[
w \leq \frac{4}{-2}
\]

This simplifies to:

\[
w \leq -2
\]

Thus, the equivalent inequality is:

\[
w \leq -2
\]