2.7 Linear inequalities and absolute value inequalities  (Page 6/11)

$\left|x+2\right|-5<2$

$\frac{-1}{2}\left|x+2\right|<4$

$\left|4x+1\right|-3>2$

$\left|x-4\right|<3$

$\left|x+2\right|\ge 5$

Solve $\left|3x+1\right|=\left|2x+3\right|$

Solve $x^2-x>12$

$\frac{x-5}{x+7}\le 0,$ $x\ne \mathrm{-7}$

$p=-x^2+130x-3000$ is a profit formula for a small business. Find the set of x -values that will keep this profit positive.

In chemistry the volume for a certain gas is given by $V=20T,$ where V is measured in cc and T is temperature in ºC. If the temperature varies between 80ºC and 120ºC, find the set of volume values.

A basic cellular package costs $20/mo. for 60 min of calling, with an additional charge of $.30/min beyond that time.. The cost formula would be $$C=\text{\$}20+.30(x-60).$$ If you have to keep your bill lower than $50, what is the maximum calling minutes you can use?

$4x-3y=12$

$2y-4=3x$

$5x=3y-12$

$2x-5y=7$

$\left(\mathrm{-2},5\right)\left(4,\mathrm{-1}\right)$

$\left(\mathrm{-12},\mathrm{-3}\right)\left(\mathrm{-1},5\right)$

Find the distance between the two points $(\mathrm{-71,432})$ and $\text{(511,218)}$ using your calculator, and round your answer to the nearest thousandth.

$\left(\mathrm{-1},5\right)\text{ and }\left(4,6\right)$

$\left(\mathrm{-13},5\right)\text{ and }\left(17,18\right)$

$y=\frac{1}{2}x+4$

$4x-3y=6$

$5x+2=7x-8$

$3(x+2)-10=x+4$

$7x-3=5$

$12-5(x+1)=2x-5$

$\frac{2x}{3}-\frac{3}{4}=\frac{x}{6}+\frac{21}{4}$

$\frac{x}{x^2-9}+\frac{4}{x+3}=\frac{3}{x^2-9}$ $x\ne 3,\mathrm{-3}$

$\frac{1}{2}+\frac{2}{x}=\frac{3}{4}$

Passes through these two points: $\left(\mathrm{-2},1\right)\text{,}\left(4,2\right).$

Passes through the point $\left(-3,4\right)$ and has a slope of $\frac{-1}{3}.$

Passes through the point $\left(-3,4\right)$ and is parallel to the graph $y=\frac{2}{3}x+5.$

Passes through these two points: $\left(5,1\right)\text{,}\left(5,7\right).$

The number of males in the classroom is five more than three times the number of females. If the total number of students is 73, how many of each gender are in the class?