Question

your answer is incorrect. solve the compound inequality. 4x - 3 ≤ 21 and 2x - 6 ≥ - 10 graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 3 to both sides of $4x - 3\leq21$:
$4x-3 + 3\leq21 + 3$, which simplifies to $4x\leq24$. Then divide both sides by 4: $x\leq6$.

Step2: Solve the second inequality

Add 6 to both sides of $2x - 6\geq - 10$:
$2x-6 + 6\geq - 10+6$, which simplifies to $2x\geq - 4$. Then divide both sides by 2: $x\geq - 2$.

Answer:

The solution of the compound - inequality is $-2\leq x\leq6$. On the number - line, we mark a closed circle at $x = - 2$ and $x = 6$ and shade the region between them.