Question

question
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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.
( -2x - 4 leq -2 ) and ( -2x - 4 < -16 )

Explanation:

Step1: Solve first inequality

Start with $-2x - 4 \leq -2$.
Add 4 to both sides:
$-2x - 4 + 4 \leq -2 + 4$
$-2x \leq 2$
Divide by $-2$ (reverse inequality):
$x \geq -1$

Step2: Solve second inequality

Start with $-2x - 4 < -16$.
Add 4 to both sides:
$-2x - 4 + 4 < -16 + 4$
$-2x < -12$
Divide by $-2$ (reverse inequality):
$x > 6$

Step3: Find intersection of solutions

We need $x \geq -1$ and $x > 6$. The overlap of these sets is all $x$ greater than 6.

Answer:

$x > 6$

To graph this on a number line: Draw an open circle at 6, and shade all values to the right of 6.