# 5.10 Proficiency exam

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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules (<link document="m21980"/>) and (<link document="m21979"/>)). This module contains the proficiency exam for the chapter "Solving Linear Equations and Inequalities".

## Proficiency exam

Solve the equations and inequalities for the following problems.

( [link] ) $x+8=14$

$x=6$

( [link] ) $6a+3=-10$

$a=\frac{-13}{6}$

( [link] ) $\frac{-3a}{8}=6$

$a=-16$

( [link] ) $\frac{x}{-2}+16=11$

$x=10$

( [link] ) $\frac{y-9}{4}+6=3$

$y=-3$

( [link] ) $5b-8=7b+12$

$b=-10$

( [link] ) $3\left(2a+4\right)=2\left(a+3\right)$

$a=-\frac{3}{2}$

( [link] ) $5\left(y+3\right)-\left(2y-1\right)=-5$

$y=-7$

( [link] ) $\frac{-\left(4x+3-5x\right)}{3}=2$

$x=9$

( [link] ) Solve $2p-6q+1=-2\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}p$ .

$p=\frac{6q-3}{2}$

( [link] ) Solve $p=\frac{nRT}{V}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}T$ .

$T=\frac{Vp}{nR}$

( [link] ) Solve for $△$ .

( [link] ) $a-8\ge 4$

$a\ge 12$

( [link] ) $-3a+1<-5$

$a>2$

( [link] ) $-2\left(a+6\right)\le -a+11$

$a\ge -23$

( [link] ) $\frac{-4x-3}{3}>-9$

$x<6$

Translate the phrases or sentences into mathematical expressions or equations for the following problems.

$3+2a$

( [link] ) Eight less than two thirds of a number.

$\frac{2}{3}x-8$

( [link] ) Two more than four times a number.

$2+4x$

( [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.

$\left(3,13\right)$