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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] ) 6 a + 3 = 10

a = 13 6

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( [link] ) 3 a 8 = 6

a = 16

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( [link] ) x 2 + 16 = 11

x = 10

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( [link] ) y 9 4 + 6 = 3

y = 3

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

b = 10

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( [link] ) 3 ( 2 a + 4 ) = 2 ( a + 3 )

a = 3 2

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( [link] ) 5 ( y + 3 ) ( 2 y 1 ) = 5

y = 7

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( [link] ) ( 4 x + 3 5 x ) 3 = 2

x = 9

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( [link] ) Solve 2 p 6 q + 1 = 2 for p .

p = 6 q 3 2

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( [link] ) Solve p = n R T V for T .

T = V p n R

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( [link] ) 3 a + 1 < 5

a > 2

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( [link] ) 2 ( a + 6 ) a + 11

a 23

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( [link] ) 4 x 3 3 > 9

x < 6

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

( [link] ) Three added to twice a number.

3 + 2 a

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

2 3 x 8

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

2 + 4 x

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

2 x ( x 3 ) = 12

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( [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.

x 5 x + 10 = 6 x

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Solve the following problems.

( [link] ) Eight percent of a number is 1.2 . What is the number?

x = 15

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( [link] ) Three consecutive odd integers sum to 38. What are they?

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

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

x < 4

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

( 3 , 13 )

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Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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