Question

solve for $x$ and graph the solution on the number line below.
$-36 < -5x - 6$ or $-5x - 6 < -46$
answer attempt 2 out of 10
inequality notation:
number line:

Explanation:

Step1: Solve the first - inequality

Add 6 to both sides of $-36 < - 5x-6$:
$-36 + 6< - 5x-6 + 6$, which simplifies to $-30 < - 5x$.
Divide both sides by - 5. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $\frac{-30}{-5}>\frac{-5x}{-5}$, resulting in $6 > x$ or $x < 6$.

Step2: Solve the second - inequality

Add 6 to both sides of $-5x - 6 < - 46$:
$-5x-6 + 6 < - 46+6$, which simplifies to $-5x < - 40$.
Divide both sides by - 5. Since we are dividing by a negative number, the inequality sign changes. So $\frac{-5x}{-5}>\frac{-40}{-5}$, resulting in $x > 8$.

Answer:

Inequality Notation: $x < 6$ or $x > 8$
Number - line: Mark an open circle at 6 and shade to the left, mark an open circle at 8 and shade to the right.