Question

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank.
-29 > -4x + 3 or -4x + 3 ≥ -37
answer attempt 2 out of 2
inequality notation:
number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked

Explanation:

Step1: Solve first inequality

Start with $-29 > -4x + 3$. Subtract 3 from both sides:
$-29 - 3 > -4x$
$-32 > -4x$
Divide by -4 (reverse inequality):
$\frac{-32}{-4} < x$
$8 < x$ or $x > 8$

Step2: Solve second inequality

Start with $-4x + 3 \geq -37$. Subtract 3 from both sides:
$-4x \geq -37 - 3$
$-4x \geq -40$
Divide by -4 (reverse inequality):
$x \leq \frac{-40}{-4}$
$x \leq 10$

Step3: Combine solutions

The compound inequality is "or", so combine $x > 8$ and $x \leq 10$.

Answer:

Inequality Notation: $8 < x \leq 10$

For the number line:

• Draw an open circle at 8, a closed circle at 10, and shade the region between 8 and 10 (including 10, excluding 8).