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. (-4x + 8 < -32) or (-4x + 8 < -40)
answer
inequality notation:
number line:

Explanation:

Step1: Solve first inequality

Subtract 8 from both sides:
$-4x + 8 - 8 < -32 - 8$
$-4x < -40$
Divide by -4 (reverse inequality):
$x > 10$

Step2: Solve second inequality

Subtract 8 from both sides:
$-4x + 8 - 8 < -40 - 8$
$-4x < -48$
Divide by -4 (reverse inequality):
$x > 12$

Step3: Combine "or" solutions

Since $x > 12$ is a subset of $x > 10$, the combined solution is the broader set.

Answer:

Inequality Notation:

$x > 10$

Number Line:

Draw an open circle at 10, with an arrow pointing to the right (toward positive infinity) along the given number line.