Solve the inequality 6−2x+1<−3(5−x)+7 .(1 point) x>

Answer 1

To solve the inequality \( 6 - 2x + 1 < -3(5 - x) + 7 \), let's simplify both sides step by step.

1. Start by simplifying the left side: \[ 6 - 2x + 1 = 7 - 2x \]

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

3. Rewrite the inequality with these simplifications: \[ 7 - 2x < 3x - 8 \]

4. Next, let's get all the terms involving \( x \) on one side and the constant terms on the other side. We can add \( 2x \) to both sides: \[ 7 < 3x + 2x - 8 \] \[ 7 < 5x - 8 \]

5. Now add \( 8 \) to both sides: \[ 7 + 8 < 5x \] \[ 15 < 5x \]

6. Finally, divide both sides by \( 5 \): \[ \frac{15}{5} < x \] \[ 3 < x \]

This can also be written as: \[ x > 3 \]

Thus, the solution to the inequality is: \[ \boxed{x > 3} \]