Question

1. solve and graph: 52 < 4 + 6a ≤ 64
2. solve and graph: 5 - 10a ≤ 45 or a + 4 < -1
3. solve and graph: 5a - 10 ≤ -45 and -1 - a ≥ -4

Explanation:

Step1: Solve the first inequality $5a - 10\leq - 45$

Add 10 to both sides: $5a\leq - 45 + 10$, so $5a\leq - 35$. Then divide both sides by 5, we get $a\leq - 7$.

Step2: Solve the second inequality $-1 - a\geq - 4$

Add 1 to both sides: $-a\geq - 4 + 1$, so $-a\geq - 3$. Multiply both sides by - 1 and reverse the inequality sign, we have $a\leq3$.

Step3: Find the intersection

Since we have $a\leq - 7$ and $a\leq3$, the solution of the compound - inequality (because of AND) is $a\leq - 7$.

Step4: Graph on the number line

On the given number line, we mark a closed circle at - 7 (because the inequality is $\leq$) and shade to the left of - 7.

Answer:

The solution of the inequality $5a - 10\leq - 45$ and $-1 - a\geq - 4$ is $a\leq - 7$. On the number - line, mark a closed circle at - 7 and shade to the left.