Question

solve each inequality and graph its solution.

1. -12>x - 7
2. n - 6≤ - 14
3. a - 17> - 16
4. 3 + v≤ - 9
5. - 3x>3
6. \frac{k}{4}< - 4

Explanation:

Step1: Solve -12>x - 7

Add 7 to both sides.
$-12 + 7>x-7 + 7$
$-5>x$ or $x < - 5$

Step2: Solve n - 6≤ - 14

Add 6 to both sides.
$n-6 + 6\leq-14 + 6$
$n\leq-8$

Step3: Solve a - 17>-16

Add 17 to both sides.
$a-17 + 17>-16 + 17$
$a>1$

Step4: Solve 3 + v≤ - 9

Subtract 3 from both sides.
$3 + v-3\leq-9-3$
$v\leq-12$

Step5: Solve -3x>3

Divide both sides by - 3 and reverse the inequality sign.
$\frac{-3x}{-3}<\frac{3}{-3}$
$x < - 1$

Step6: Solve $\frac{k}{4}<-4$

Multiply both sides by 4.
$\frac{k}{4}\times4<-4\times4$
$k < - 16$

Answer:

1. $x < - 5$
2. $n\leq-8$
3. $a>1$
4. $v\leq-12$
5. $x < - 1$
6. $k < - 16$