Question

solve the compound inequality. 3x - 4 ≤ - 7 and 3x + 3 ≥ - 12. graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Solve $3x - 4\leq - 7$. Add 4 to both sides: $3x\leq - 7 + 4$, so $3x\leq - 3$. Then divide both sides by 3: $x\leq - 1$.

Step2: Solve the second inequality

Solve $3x+3\geq - 12$. Subtract 3 from both sides: $3x\geq - 12 - 3$, so $3x\geq - 15$. Then divide both sides by 3: $x\geq - 5$.

Step3: Determine the compound - inequality solution

The compound - inequality solution is $-5\leq x\leq - 1$.

Step4: Graph on the number line

On the number line, draw a closed circle at $x = - 5$ and a closed circle at $x=-1$, and shade the region between them.

Answer:

The solution of the compound inequality is $-5\leq x\leq - 1$. On the number line, mark closed circles at $-5$ and $-1$ and shade the region between them.