Question

Solve the inequality 6−2x+1<−3(5−x)+7

Answer 1

To solve the inequality \( 6 - 2x + 1 < -3(5 - x) + 7 \), we can start by simplifying both sides.

1. **Simplify the left side:**
\[
6 - 2x + 1 = 7 - 2x
\]

2. **Simplify the right side:**
\[
-3(5 - x) + 7 = -15 + 3x + 7 = 3x - 8
\]

Now, we can rewrite the inequality as:
\[
7 - 2x < 3x - 8
\]

3. **Rearrange the inequality:**
First, add \( 2x \) to both sides:
\[
7 < 3x + 2x - 8
\]
Simplifying gives:
\[
7 < 5x - 8
\]

4. Next, add \( 8 \) to both sides:
\[
7 + 8 < 5x
\]
Which simplifies to:
\[
15 < 5x
\]

5. Finally, divide both sides by \( 5 \):
\[
3 < x
\]
or equivalently:
\[
x > 3
\]

The solution to the inequality \( 6 - 2x + 1 < -3(5 - x) + 7 \) is:
\[
x > 3
\]