Question

common core spiral review
solve each inequality. graph the solution set on a number line. 7.ee.4b

1. a - 5 < 2
2. x - 9 ≥ -12
3. 5y ≤ -30
4. $\frac{n}{4}$ > -2

Explanation:

Step1: Solve inequality 26

Add 5 to both sides of $a - 5<2$.
$a-5 + 5<2 + 5$, so $a<7$.
On number - line, use an open circle at 7 and shade to the left.

Step2: Solve inequality 27

Add 9 to both sides of $x - 9\geq - 12$.
$x-9 + 9\geq - 12+9$, so $x\geq - 3$.
On number - line, use a closed circle at - 3 and shade to the right.

Step3: Solve inequality 28

Divide both sides of $5y\leq - 30$ by 5.
$\frac{5y}{5}\leq\frac{-30}{5}$, so $y\leq - 6$.
On number - line, use a closed circle at - 6 and shade to the left.

Step4: Solve inequality 29

Multiply both sides of $\frac{n}{4}>-2$ by 4.
$\frac{n}{4}\times4>-2\times4$, so $n > - 8$.
On number - line, use an open circle at - 8 and shade to the right.

Answer:

1. Solution: $a<7$, graph: open circle at 7, shade left.
2. Solution: $x\geq - 3$, graph: closed circle at - 3, shade right.
3. Solution: $y\leq - 6$, graph: closed circle at - 6, shade left.
4. Solution: $n > - 8$, graph: open circle at - 8, shade right.