Compound Inequalities Practice AK

Solve the inequalities:

1.

$\eqalign{13>x-1>5\\ \mathbf{14>x>6}}$

2.

$\eqalign{-2<y+5<10\\\mathbf{-7<y<5}}$

3.

$\eqalign{-15 \leq 2z-3 \leq 6\\12 \leq 2z \leq 9\\\mathbf{-6 \leq z \leq 4.5}}$

4.

$\eqalign{22>4x+10>18\\12>4x>8\\\mathbf{3>x>2}}$

5.

$\eqalign{-1<-3a+7<90\\-8<-3a<83\\\mathbf{\dfrac{8}{3}>a>\dfrac{-83}{3}}}$

6.

$\eqalign{3-1 \ge 6b-1 \ge 1\\2 \ge 6b-1 \ge 1\\3 \ge 6b \ge 2\\\mathbf{\dfrac{1}{2} \ge b \ge \dfrac{1}{3}}}$

7.

$\eqalign{40>-8c+2>6-10\\38>-8c>-6\\\mathbf{\dfrac{-38}{8}<c<\dfrac{3}{4}}}$

8.

$\eqalign{140+6>12v+2>62\\144>12v>60\\\mathbf{12>v>5}}$

9.

$\eqalign{15<-x+10<54\\5<-x<34\\\mathbf{-5>x>-34}}$

10.

$\eqalign{32 \ge -14g-10 \ge 4\\42 \ge -14g \ge 14\\\mathbf{-3 \ge g \ge -1}}$