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Solving Linear Equations and Inequalities: Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: 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 ((Reference)) and ((Reference))). 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.

Exercise 1

((Reference)) x+8=14 x+8=14

Solution

x=6 x=6

Exercise 2

((Reference)) 6a+3=−10 6a+3=−10

Solution

a= −13 6 a= −13 6

Exercise 3

((Reference)) −3a 8 =6 −3a 8 =6

Solution

a=−16 a=−16

Exercise 4

((Reference)) x −2 +16=11 x −2 +16=11

Solution

x=10 x=10

Exercise 5

((Reference)) y−9 4 +6=3 y−9 4 +6=3

Solution

y=−3 y=−3

Exercise 6

((Reference)) 5b−8=7b+12 5b−8=7b+12

Solution

b=−10 b=−10

Exercise 7

((Reference)) 3(2a+4)=2(a+3) 3(2a+4)=2(a+3)

Solution

a=− 3 2 a=− 3 2

Exercise 8

((Reference)) 5(y+3)−(2y−1)=−5 5(y+3)−(2y−1)=−5

Solution

y=−7 y=−7

Exercise 9

((Reference)) −(4x+3−5x) 3 =2 −(4x+3−5x) 3 =2

Solution

x=9 x=9

Exercise 10

((Reference)) Solve 2p−6q+1=−2 for p 2p−6q+1=−2 for p .

Solution

p= 6q−3 2 p= 6q−3 2

Exercise 11

((Reference)) Solve p= nRT V  for T p= nRT V  for T .

Solution

T= Vp nR T= Vp nR

Exercise 12

((Reference)) Solve The sum of triangle and square over star is equal to delta. for △ △ .

Solution

The triangle is equal to the product of star and delta, minus square.

Exercise 13

((Reference)) a−8≥4 a−8≥4

Solution

a≥12 a≥12

Exercise 14

((Reference)) −3a+1<−5 −3a+1<−5

Solution

a>2 a>2

Exercise 15

((Reference)) −2(a+6)≤−a+11 −2(a+6)≤−a+11

Solution

a≥−23 a≥−23

Exercise 16

((Reference)) −4x−3 3 >−9 −4x−3 3 >−9

Solution

x<6 x<6

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

Exercise 17

((Reference)) Three added to twice a number.

Solution

3+2a 3+2a

Exercise 18

((Reference)) Eight less than two thirds of a number.

Solution

2 3 x−8 2 3 x−8

Exercise 19

((Reference))Two more than four times a number.

Solution

2+4x 2+4x

Exercise 20

((Reference)) A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.

Solution

2x( x 3 )=12 2x( x 3 )=12

Exercise 21

((Reference)) 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.

Solution

x−5 x+10 =6x x−5 x+10 =6x

Solve the following problems.

Exercise 22

((Reference)) Eight percent of a number is 1.2 1.2 . What is the number?

Solution

x=15 x=15

Exercise 23

((Reference)) Three consecutive odd integers sum to 38. What are they?

Solution

There are no three consecutive odd integers that add to 38.

Exercise 24

((Reference)) Five more than three times a number is strictly less than seventeen. What is the number?

Solution

x<4 x<4

Exercise 25

((Reference)) Solve y=8x−11 y=8x−11 for y if x=3 y if x=3 , and write the solution as an ordered pair.

Solution

( 3,13 ) ( 3,13 )

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