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. ( 3x + 2 > -16 ) and ( 3x + 2 > -4 ) answer inequality notation:

Explanation:

Step1: Solve first inequality

Subtract 2 from both sides:
$3x + 2 - 2 > -16 - 2$
$3x > -18$
Divide by 3:
$\frac{3x}{3} > \frac{-18}{3}$
$x > -6$

Step2: Solve second inequality

Subtract 2 from both sides:
$3x + 2 - 2 > -4 - 2$
$3x > -6$
Divide by 3:
$\frac{3x}{3} > \frac{-6}{3}$
$x > -2$

Step3: Find intersection of solutions

For "and", take the stricter inequality. Since $x > -2$ includes all values that satisfy $x > -6$ but not vice versa, the combined solution is $x > -2$.

Answer:

Inequality Notation: $x > -2$

For the number line: Draw an open circle at $-2$, then shade all regions to the right of $-2$.