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Solve the equations and inequalities for the following problems.
( [link] ) Solve $2p-6q+1=-2\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}p$ .
$p=\frac{6q-3}{2}$
( [link] ) Solve $p=\frac{nRT}{V}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T$ .
$T=\frac{Vp}{nR}$
Translate the phrases or sentences into mathematical expressions or equations for the following problems.
( [link] ) Eight less than two thirds of a number.
$\frac{2}{3}x-8$
( [link] ) A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.
$2x\left({x}^{3}\right)=12$
( [link] ) A number is decreased by five and that result is divided by ten more than the original number. The result is six times the original number.
$\frac{x-5}{x+10}=6x$
Solve the following problems.
( [link] ) Eight percent of a number is $1.2$ . What is the number?
$x=15$
( [link] ) Three consecutive odd integers sum to 38. What are they?
There are no three consecutive odd integers that add to 38.
( [link] ) Five more than three times a number is strictly less than seventeen. What is the number?
$x<4$
( [link] ) Solve $y=8x-11$ for $y\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}x=3$ , and write the solution as an ordered pair.
$\left(3,13\right)$
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