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In the following exercises, solve the following equations with constants on both sides.

32 = −4 9 n

n = −4

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Solve an Equation with Variables on Both Sides

In the following exercises, solve the following equations with variables on both sides.

4 x 3 8 = 3 x

x = 3 8

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Solve an Equation with Variables and Constants on Both Sides

In the following exercises, solve the following equations with variables and constants on both sides.

5 n 20 = −7 n 80

n = −5

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5 8 c 4 = 3 8 c + 4

c = 32

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Section 2.4 Use a General Strategy for Solving Linear Equations

Solve Equations Using the General Strategy for Solving Linear Equations

In the following exercises, solve each linear equation.

9 ( 2 p 5 ) = 72

p = 13 2

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8 + 3 ( n 9 ) = 17

n = 12

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23 3 ( y 7 ) = 8

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1 3 ( 6 m + 21 ) = m 7

m = −14

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4 ( 3.5 y + 0.25 ) = 365

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0.25 ( q 8 ) = 0.1 ( q + 7 )

q = 18

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8 ( r 2 ) = 6 ( r + 10 )

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5 + 7 ( 2 5 x ) = 2 ( 9 x + 1 )
( 13 x 57 )

x = −1

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( 9 n + 5 ) ( 3 n 7 )
= 20 ( 4 n 2 )

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2 [ −16 + 5 ( 8 k 6 ) ]
= 8 ( 3 4 k ) 32

k = 3 4

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Classify Equations

In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.

17 y 3 ( 4 2 y ) = 11 ( y 1 )
+ 12 y 1

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9 u + 32 = 15 ( u 4 )
3 ( 2 u + 21 )

contradiction; no solution

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−8 ( 7 m + 4 ) = −6 ( 8 m + 9 )

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21 ( c 1 ) 19 ( c + 1 )
= 2 ( c 20 )

identity; all real numbers

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Section 2.5 Solve Equations with Fractions and Decimals

Solve Equations with Fraction Coefficients

In the following exercises, solve each equation with fraction coefficients.

1 3 x + 1 5 x = 8

x = 15

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3 4 a 1 3 = 1 2 a 5 6

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1 2 ( k 3 ) = 1 3 ( k + 16 )

k = 41

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5 y 1 3 + 4 = −8 y + 4 6

y = −1

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Solve Equations with Decimal Coefficients

In the following exercises, solve each equation with decimal coefficients.

0.8 x 0.3 = 0.7 x + 0.2

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0.36 u + 2.55 = 0.41 u + 6.8

u = −85

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0.6 p 1.9 = 0.78 p + 1.7

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0.6 p 1.9 = 0.78 p + 1.7

d = −20

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Section 2.6 Solve a Formula for a Specific Variable

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Natalie drove for 7 1 2 hours at 60 miles per hour. How much distance did she travel?

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Mallory is taking the bus from St. Louis to Chicago. The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour. How long will the bus ride be?

5 hours

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Aaron’s friend drove him from Buffalo to Cleveland. The distance is 187 miles and the trip took 2.75 hours. How fast was Aaron’s friend driving?

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Link rode his bike at a steady rate of 15 miles per hour for 2 1 2 hours. How much distance did he travel?

37.5 miles

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Solve a Formula for a Specific Variable

In the following exercises, solve.

Use the formula. d = r t to solve for t
when d = 510 and r = 60
in general

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Use the formula. d = r t to solve for r
when when d = 451 and t = 5.5
in general

r = 82 mph ; r = D t

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Use the formula A = 1 2 b h to solve for b
when A = 390 and h = 26
in general

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Use the formula A = 1 2 b h to solve for h
when A = 153 and b = 18
in general

h = 17 h = 2 A b

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Use the formula I = P r t to solve for the principal, P for
I = $ 2 , 501 , r = 4.1 % ,
t = 5 years
in general

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Solve the formula 4 x + 3 y = 6 for y
when x = −2
in general

y = 14 3 y = 6 4 x 3

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Solve 180 = a + b + c for c .

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Solve the formula V = L W H for H .

H = V L W

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Section 2.7 Solve Linear Inequalities

Graph Inequalities on the Number Line

In the following exercises, graph each inequality on the number line.


x 4
x > 2
x < 1

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x > 0
x < 3
x −1


  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 0 is graphed on the number line, with an open parenthesis at x equals 0, and a dark line extending to the right of the parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 3 is graphed on the number line, with an open parenthesis at x equals negative 3, and a dark line extending to the left of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a dark line extending to the right of the bracket.
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In the following exercises, graph each inequality on the number line and write in interval notation.


x < 1
x −2.5
x 5 4

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x > 2
x 1.5
x 5 3


  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 2 comma infinity, parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 1.5, bracket.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 5/3 is graphed on the number line, with an open bracket at x equals 5/3, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 5/3 comma infinity, parenthesis.
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Solve Inequalities using the Subtraction and Addition Properties of Inequality

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

Solve Inequalities using the Division and Multiplication Properties of Inequality

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

Solve Inequalities That Require Simplification

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

9 h 7 ( h 1 ) 4 h 23

At the top of this figure is the solution to the inequality: h is greater than or equal to 15. Below this is a number line ranging from 13 to 17 with tick marks for each integer. The inequality h is greater than or equal to 15 is graphed on the number line, with an open bracket at h equals 15, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 15 comma infinity, parenthesis.

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5 n 15 ( 4 n ) < 10 ( n 6 ) + 10 n

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3 8 a 1 12 a > 5 12 a + 3 4

At the top of this figure is the solution to the inequality: a is less than negative 6. Below this is a number line ranging from negative 8 to negative 4 with tick marks for each integer. The inequality a is less than negative 6 is graphed on the number line, with an open parenthesis at a equals negative 6, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 6, parenthesis.

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Translate to an Inequality and Solve

In the following exercises, translate and solve. Then write the solution in interval notation and graph on the number line.

Five more than z is at most 19.

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Three less than c is at least 360.

At the top of this figure is the inequality c minus 3 is greater than or equal to 360. To the right of this is the solution to the inequality: c is greater than or equal to 363. To the right of the solution is the solution written in interval notation: bracket, 363 comma infinity, parenthesis. Below all of this is a number line ranging from 361 to 365 with tick marks for each integer. The inequality c is greater than or equal to 363 is graphed on the number line, with an open bracket at c equals 363, and a dark line extending to the right of the bracket.

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Nine times n exceeds 42.

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Negative two times a is no more than 8.

At the top of this figure is the inequality negative 2a is less than or equal to 8. To the right of this is the solution to the inequality: a is greater than or equal to negative 4. To the right of the solution is the solution written in interval notation: bracket, negative 4 comma infinity, parenthesis. Below all of this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality a is greater than or equal to negative 4 is graphed on the number line, with an open bracket at a equals negative 4, and a dark line extending to the right of the bracket.

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Everyday math

Describe how you have used two topics from this chapter in your life outside of your math class during the past month.

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Chapter 2 practice test

Determine whether each number is a solution to the equation 6 x 3 = x + 20 .


5
23 5

no yes

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In the following exercises, solve each equation.

−8 x 15 + 9 x 1 = −21

x = −5

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10 y = −5 y 60

y = −4

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9 m 2 4 m m = 42 8

m = 9

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( d 9 ) = 23

d = −14

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1 4 ( 12 m 28 ) = 6 2 ( 3 m 1 )

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2 ( 6 x 5 ) 8 = −22

x = 1 3

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8 ( 3 a 5 ) 7 ( 4 a 3 ) = 20 3 a

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1 4 p 1 3 = 1 2

p = 10 3

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0.1 d + 0.25 ( d + 8 ) = 4.1

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14 n 3 ( 4 n + 5 ) = −9 + 2 ( n 8 )

contradiction; no solution

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9 ( 3 u 2 ) 4 [ 6 8 ( u 1 ) ] = 3 ( u 2 )

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Solve the formula x 2 y = 5 for y
when x = −3
in general

y = 4 y = 5 x 2

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In the following exercises, graph on the number line and write in interval notation.

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

3 c 10 ( c 2 ) < 5 c + 16

This figure is a number line ranging from negative 2 to 3 with tick marks for each integer. The inequality c is greater than 1/3 is graphed on the number line, with an open parenthesis at c equals 1/3, and a dark line extending to the right of the parenthesis. Below the number line is the solution: c is greater than 1/3. To the right of the solution is the solution written in interval notation: parenthesis, 1/3 comma infinity, parenthesis

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In the following exercises, translate to an equation or inequality and solve.

4 less than twice x is 16.

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Fifteen more than n is at least 48.

n + 15 48 ; n 33

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Samuel paid $25.82 for gas this week, which was $3.47 less than he paid last week. How much had he paid last week?

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Jenna bought a coat on sale for $120, which was 2 3 of the original price. What was the original price of the coat?

120 = 2 3 p ; The original price was $180.

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Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2 3 hours, what was the speed of the bus?

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Questions & Answers

what is mutation
Janga Reply
what is a cell
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classification of plants, gymnosperm features.
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What is Atoms
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urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
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State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
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how is urine formed in human
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
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Definition of respiration
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respiration is the process in which we breath in oxygen and breath out carbon dioxide
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in the mouth
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stimulates the follicle to release the mature ovum into the oviduct
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endocrine secrete hormone and regulate body process
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Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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Biology is the study of how living organisms live and survive in a specific environment
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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