Question

Solve the inequality.

k + 4 – 2(k – 12) > 0


k < –20


k < 28


k > –20


k > 28

Answer 1

Let's solve the inequality step by step.

The given inequality is:

\[ k + 4 - 2(k - 12) > 0 \]

First, distribute the \(-2\):

\[ k + 4 - 2k + 24 > 0 \]

Next, combine like terms:

\[ (k - 2k) + (4 + 24) > 0 \]

This simplifies to:

\[ -k + 28 > 0 \]

Now, isolate \(k\) by subtracting 28 from both sides:

\[ -k > -28 \]

Now, multiply both sides by \(-1\) and reverse the inequality sign:

\[ k < 28 \]

Thus, the solution to the inequality is:

\[ k < 28 \]

So, the correct answer is:

**k < 28**