Question

solve each compound inequality and graph the solution. see examples 2 and 3 19. $2x + 5 > -3$ and $4x + 7 < 15$ 20. $2x - 5 > 3$ or $-4x + 7 < -25$ 21. $2x - 5 > 3$ and $-4x + 7 < -25$ 22. $-x + 1 > -2$ or $6(2x - 3) geq -6$

Explanation:

Step1: Solve $-x + 1 > -2$

Subtract 1 from both sides:
$-x > -2 - 1$
$-x > -3$
Multiply by -1 (reverse inequality):
$x < 3$

Step2: Solve $6(2x - 3) \geq -6$

Divide both sides by 6:
$2x - 3 \geq \frac{-6}{6}$
$2x - 3 \geq -1$
Add 3 to both sides:
$2x \geq -1 + 3$
$2x \geq 2$
Divide by 2:
$x \geq 1$

Step3: Combine "or" solutions

The compound inequality uses "or", so we combine all values that satisfy either inequality. All real numbers satisfy either $x < 3$ or $x \geq 1$.

Answer:

All real numbers, or in interval notation $(-\infty, \infty)$

Graph Description:

A number line with the entire line shaded (since every real number is part of the solution set), with no open/closed endpoints needed as all values are included.