Question

Consider the inequality.

−2x+5>7

Correctly order the steps to solve the inequality.

(3 points)
.
Step 1.
Step 2.
Step 3.

Answer 1

To solve the inequality \(-2x + 5 > 7\), here is the correct order of steps:

**Step 1:** Subtract 5 from both sides.
\[
-2x + 5 - 5 > 7 - 5
\]
which simplifies to:
\[
-2x > 2
\]

**Step 2:** Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number.
\[
\frac{-2x}{-2} < \frac{2}{-2}
\]
which simplifies to:
\[
x < -1
\]

**Step 3:** Write the solution in interval notation or make a conclusion based on the inequality.
Solution: \(x < -1\) can be written in interval notation as \((-∞, -1)\).

So, the order of steps is:
1. Step 1: Subtract 5 from both sides.
2. Step 2: Divide both sides by -2 (reverse the inequality).
3. Step 3: Write the final result or solution.