Question

Solve for x
.

−5(x−4)≥2(1−x)

Move the correct answer to each box. Not all answers will be used.

The solution of the inequality is x

Answer 1

To solve the inequality \(-5(x-4) \geq 2(1-x)\), we will first distribute the numbers on both sides.

1. Distribute -5 and 2:

\[
-5x + 20 \geq 2 - 2x
\]

2. To get all the \(x\) terms on one side, we can add \(2x\) to both sides:

\[
-5x + 2x + 20 \geq 2
\]

This simplifies to:

\[
-3x + 20 \geq 2
\]

3. Next, subtract 20 from both sides:

\[
-3x \geq 2 - 20
\]

This simplifies to:

\[
-3x \geq -18
\]

4. Finally, divide both sides by -3. Remember that when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign:

\[
x \leq 6
\]

So the solution of the inequality is \(x \leq 6\).

In summary, the solution of the inequality is \(x \leq 6\). You can fill in the boxes with the appropriate parts.