Question

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.
( 2 > -x - 6 ) and ( -x - 6 leq -3 )

Explanation:

Step1: Solve first inequality

Start with $2 > -x - 6$.
Add 6 to both sides: $2 + 6 > -x$
$8 > -x$
Multiply by -1 (reverse inequality): $x > -8$

Step2: Solve second inequality

Start with $-x - 6 \leq -3$.
Add 6 to both sides: $-x \leq -3 + 6$
$-x \leq 3$
Multiply by -1 (reverse inequality): $x \geq -3$

Step3: Find intersection of solutions

We need $x > -8$ and $x \geq -3$. The overlapping solution is the stricter condition.

Answer:

$x \geq -3$

To graph this on the number line:

• Place a closed circle at $-3$ (since the inequality includes equality)
• Draw a solid line extending to the right from $-3$ to represent all values greater than or equal to $-3$.