2.7 Solve linear inequalities  (Page 6/8)

ⓐ $x\le 2$
ⓑ $x>-1$
ⓒ $x<0$

ⓐ $x>1$
ⓑ $x<-2$
ⓒ $x\ge \mathrm{-3}$

ⓐ $x\ge \mathrm{-3}$
ⓑ $x<4$
ⓒ $x\le -2$

ⓐ $x\le 0$
ⓑ $x>-4$
ⓒ $x\ge \mathrm{-1}$

ⓐ $x<-2$
ⓑ $x\ge \mathrm{-3.5}$
ⓒ $x\le \frac{2}{3}$

ⓐ $x>3$
ⓑ $x\le -0.5$
ⓒ $x\ge \frac{1}{3}$

ⓐ $x\ge \mathrm{-4}$
ⓑ $x<2.5$
ⓒ $x>-\frac{3}{2}$

ⓐ $x\le 5$
ⓑ $x\ge \mathrm{-1.5}$
ⓒ $x<-\frac{7}{3}$

$n-11<33$

$m-45\le 62$

$u+25>21$

$v+12>3$

$a+\frac{3}{4}\ge \frac{7}{10}$

$b+\frac{7}{8}\ge \frac{1}{6}$

$f-\frac{13}{20}<-\frac{5}{12}$

$g-\frac{11}{12}<-\frac{5}{18}$

$8x>72$

$6y<48$

$7r\le 56$

$9s\ge 81$

$\mathrm{-5}u\ge 65$

$\mathrm{-8}v\le 96$

$\mathrm{-9}c<126$

$\mathrm{-7}d>105$

$20>\frac{2}{5}h$

$40<\frac{5}{8}k$

$\frac{7}{6}j\ge 42$

$\frac{9}{4}g\le 36$

$\frac{a}{\mathrm{-3}}\le 9$

$\frac{b}{\mathrm{-10}}\ge 30$

$\mathrm{-25}<\frac{p}{\mathrm{-5}}$

$\mathrm{-18}>\frac{q}{\mathrm{-6}}$

$9t\ge \mathrm{-27}$

$7s<-28$

$\frac{2}{3}y>-36$

$\frac{3}{5}x\le -45$

$4v\ge 9v-40$

$5u\le 8u-21$

$13q<7q-29$

$9p>14p-18$

$12x+3(x+7)>10x-24$

$9y+5(y+3)<4y-35$

$6h-4(h-1)\le 7h-11$

$4k-(k-2)\ge 7k-26$

$8m-2\left(14-m\right)\ge \text{}7\left(m-4\right)+3m$

$6n-12\left(3-n\right)\le 9\left(n-4\right)+9n$

$\frac{3}{4}b-\frac{1}{3}b<\frac{5}{12}b-\frac{1}{2}$

$9u+5(2u-5)\ge 12(u-1)+7u$

$\frac{2}{3}g-\frac{1}{2}(g-14)\le \frac{1}{6}(g+42)$

$\frac{5}{6}a-\frac{1}{4}a>\frac{7}{12}a+\frac{2}{3}$

$\frac{4}{5}h-\frac{2}{3}\left(h-9\right)\ge \frac{1}{15}\left(2h+90\right)$

$12v+3(4v-1)\le 19(v-2)+5v$

$15k\le -40$

$35k\ge \mathrm{-77}$

$23p-2(6-5p)>3(11p-4)$

$18q-4(10-3q)<5(6q-8)$

$-\frac{9}{4}x\ge -\frac{5}{12}$

$-\frac{21}{8}y\le -\frac{15}{28}$

$c+34<-99$

$d+29>-61$

$\frac{m}{18}\ge \mathrm{-4}$

$\frac{n}{13}\le -6$

Fourteen times d is greater than 56.

Ninety times c is less than 450.

Eight times z is smaller than $\mathrm{-40}$ .

Ten times y is at most $\mathrm{-110}$ .

Three more than h is no less than 25.

Six more than k exceeds 25.

Ten less than w is at least 39.

Twelve less than x is no less than 21.

Negative five times r is no more than 95.

Negative two times s is lower than 56.

Nineteen less than b is at most $\mathrm{-22}$ .

Fifteen less than a is at least $\mathrm{-7}$ .

Safety A child’s height, h , must be at least 57 inches for the child to safely ride in the front seat of a car. Write this as an inequality.

Fighter pilots The maximum height, h , of a fighter pilot is 77 inches. Write this as an inequality.

Elevators The total weight, w , of an elevator’s passengers can be no more than 1,200 pounds. Write this as an inequality.

Shopping The number of items, n , a shopper can have in the express check-out lane is at most 8. Write this as an inequality.

Give an example from your life using the phrase ‘at least’.

Give an example from your life using the phrase ‘at most’.

Explain why it is necessary to reverse the inequality when solving $\mathrm{-5}x>10$ .

Explain why it is necessary to reverse the inequality when solving $\frac{n}{\mathrm{-3}}<12$ .