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 ($\varnothing$), leave the number line blank.\
\
$ -29 > -4x + 3 $ or $ -4x + 3 \geq -37 $\
\
answer attempt 1 out of x\
\
inequality notation: \
\
number line:\

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 uses "or", so combine $x > 8$ and $x \leq 10$.
This covers all real numbers greater than 8 and less than or equal to 10, which can be written as a single inequality.

Answer:

Inequality Notation: $8 < x \leq 10$

For the number line:

• Draw an open circle at 8 (since $x > 8$ does not include 8) and a closed circle at 10 (since $x \leq 10$ includes 10).
• Shade the region between 8 and 10, extending from the open circle at 8 to the closed circle at 10.