<< Chapter < Page Chapter >> Page >

Solve: −11 = 1 2 ( 6 p + 2 ) .

p = −4

Got questions? Get instant answers now!

Solve: 8 = 1 3 ( 9 q + 6 ) .

q = 2

Got questions? Get instant answers now!

In the next example, even after distributing, we still have fractions to clear.

Solve: 1 2 ( y 5 ) = 1 4 ( y 1 ) .

Solution

.
Distribute. .
Simplify. .
Multiply by the LCD, 4. .
Distribute. .
Simplify. .
Collect the variables to the left. .
Simplify. .
Collect the constants to the right. .
Simplify. .
Check: .
Let y = 9 . .
Finish the check on your own.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 1 5 ( n + 3 ) = 1 4 ( n + 2 ) .

n = 2

Got questions? Get instant answers now!

Solve: 1 2 ( m 3 ) = 1 4 ( m 7 ) .

m = −1

Got questions? Get instant answers now!

Solve: 5 x 3 4 = x 2 .

Solution

.
Multiply by the LCD, 4. .
Simplify. .
Collect the variables to the right. .
Simplify. .
Divide. .
Simplify. .
Check: .
Let x = 1 . .
.
.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 4 y 7 3 = y 6 .

y = 2

Got questions? Get instant answers now!

Solve: −2 z 5 4 = z 8 .

z = −2

Got questions? Get instant answers now!

Solve: a 6 + 2 = a 4 + 3 .

Solution

.
Multiply by the LCD, 12. .
Distribute. .
Simplify. .
Collect the variables to the right. .
Simplify. .
Collect the constants to the left. .
Simplify. .
Check: .
Let a = −12 . .
.
.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: b 10 + 2 = b 4 + 5 .

b = −20

Got questions? Get instant answers now!

Solve: c 6 + 3 = c 3 + 4 .

c = −6

Got questions? Get instant answers now!

Solve: 4 q + 3 2 + 6 = 3 q + 5 4 .

Solution

.
Multiply by the LCD, 4. .
Distribute. .
Simplify. .
.
.
Collect the variables to the left. .
Simplify. .
Collect the constants to the right. .
Simplify. .
Divide by 5. .
Simplify. .
Check: .
Let q = −5 . .
Finish the check on your own.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 3 r + 5 6 + 1 = 4 r + 3 3 .

r = 1

Got questions? Get instant answers now!

Solve: 2 s + 3 2 + 1 = 3 s + 2 4 .

s = −8

Got questions? Get instant answers now!

Solve equations with decimal coefficients

Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money or percentages. But decimals can also be expressed as fractions. For example, 0.3 = 3 10 and 0.17 = 17 100 . So, with an equation with decimals, we can use the same method we used to clear fractions—multiply both sides of the equation by the least common denominator.

Solve: 0.06 x + 0.02 = 0.25 x 1.5 .

Solution

Look at the decimals and think of the equivalent fractions.

0.06 = 6 100 0.02 = 2 100 0.25 = 25 100 1.5 = 1 5 10

Notice, the LCD is 100.

By multiplying by the LCD, we will clear the decimals from the equation.

.
Multiply both sides by 100. .
Distribute. .
Multiply, and now we have no more decimals. .
Collect the variables to the right. .
Simplify. .
Collect the constants to the left. .
Simplify. .
Divide by 19. .
Simplify. .
Check: Let x = 8 .
.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 0.14 h + 0.12 = 0.35 h 2.4 .

h = 12

Got questions? Get instant answers now!

Solve: 0.65 k 0.1 = 0.4 k 0.35 .

k = −1

Got questions? Get instant answers now!

The next example uses an equation that is typical of the money applications in the next chapter. Notice that we distribute the decimal before we clear all the decimals.

Solve: 0.25 x + 0.05 ( x + 3 ) = 2.85 .

Solution

.
Distribute first. .
Combine like terms. .
To clear decimals, multiply by 100. .
Distribute. .
Subtract 15 from both sides. .
Simplify. .
Divide by 30. .
Simplify. .
Check it yourself by substituting x = 9 into the original equation.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve: 0.25 n + 0.05 ( n + 5 ) = 2.95 .

n = 9

Got questions? Get instant answers now!

Solve: 0.10 d + 0.05 ( d 5 ) = 2.15 .

d = 16

Got questions? Get instant answers now!

Key concepts

  • Strategy to Solve an Equation with Fraction Coefficients
    1. Find the least common denominator of all the fractions in the equation.
    2. Multiply both sides of the equation by that LCD. This clears the fractions.
    3. Solve using the General Strategy for Solving Linear Equations.

Practice makes perfect

Solve Equations with Fraction Coefficients

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

3 4 x 1 2 = 1 4

x = 1

Got questions? Get instant answers now!

5 6 y 1 3 = 7 6

y = −1

Got questions? Get instant answers now!

5 8 b + 1 2 = 3 4

b = −2

Got questions? Get instant answers now!

2 = 1 3 x 1 2 x + 2 3 x

Got questions? Get instant answers now!

2 = 3 5 x 1 3 x + 2 5 x

x = 3

Got questions? Get instant answers now!

1 4 m 4 5 m + 1 2 m = −1

Got questions? Get instant answers now!

5 6 n 1 4 n 1 2 n = −2

n = −24

Got questions? Get instant answers now!

x + 3 4 = 1 2 x 5 4

x = −4

Got questions? Get instant answers now!

3 2 z + 1 3 = z 2 3

z = −2

Got questions? Get instant answers now!

1 2 x 1 4 = 1 12 x + 1 6

Got questions? Get instant answers now!

1 2 a 1 4 = 1 6 a + 1 12

a = 1

Got questions? Get instant answers now!

1 3 b + 1 5 = 2 5 b 3 5

Got questions? Get instant answers now!

1 3 x + 2 5 = 1 5 x 2 5

x = −6

Got questions? Get instant answers now!

1 = 1 5 ( 15 x 10 )

x = 1

Got questions? Get instant answers now!

1 4 ( p 7 ) = 1 3 ( p + 5 )

Got questions? Get instant answers now!

1 5 ( q + 3 ) = 1 2 ( q 3 )

q = 7

Got questions? Get instant answers now!

1 3 ( x + 5 ) = 5 6

x = 5 2

Got questions? Get instant answers now!

4 m + 2 6 = m 3

m = −1

Got questions? Get instant answers now!

3 p + 6 3 = p 2

p = −4

Got questions? Get instant answers now!

v 10 + 1 = v 4 2

v = 20

Got questions? Get instant answers now!

d 6 + 3 = d 8 + 2

d = −24

Got questions? Get instant answers now!

3 x + 4 2 + 1 = 5 x + 10 8

Got questions? Get instant answers now!

10 y 2 3 + 3 = 10 y + 1 9

y = −1

Got questions? Get instant answers now!

7 u 1 4 1 = 4 u + 8 5

Got questions? Get instant answers now!

3 v 6 2 + 5 = 11 v 4 5

v = 4

Got questions? Get instant answers now!

Solve Equations with Decimal Coefficients

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

0.4 x + 0.6 = 0.5 x 1.2

Got questions? Get instant answers now!

0.7 x + 0.4 = 0.6 x + 2.4

x = 20

Got questions? Get instant answers now!

0.23 x + 1.47 = 0.37 x 1.05

Got questions? Get instant answers now!

0.48 x + 1.56 = 0.58 x 0.64

x = 22

Got questions? Get instant answers now!

0.9 x 1.25 = 0.75 x + 1.75

Got questions? Get instant answers now!

1.2 x 0.91 = 0.8 x + 2.29

x = 8

Got questions? Get instant answers now!

0.05 n + 0.10 ( n + 8 ) = 2.15

Got questions? Get instant answers now!

0.05 n + 0.10 ( n + 7 ) = 3.55

n = 19

Got questions? Get instant answers now!

0.10 d + 0.25 ( d + 5 ) = 4.05

Got questions? Get instant answers now!

0.10 d + 0.25 ( d + 7 ) = 5.25

d = 10

Got questions? Get instant answers now!

0.05 ( q 5 ) + 0.25 q = 3.05

Got questions? Get instant answers now!

0.05 ( q 8 ) + 0.25 q = 4.10

q = 15

Got questions? Get instant answers now!

Everyday math

Coins Taylor has $2.00 in dimes and pennies. The number of pennies is 2 more than the number of dimes. Solve the equation 0.10 d + 0.01 ( d + 2 ) = 2 for d , the number of dimes.

Got questions? Get instant answers now!

Stamps Paula bought $22.82 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 8 less than the number of 49-cent stamps. Solve the equation 0.49 s + 0.21 ( s 8 ) = 22.82 for s , to find the number of 49-cent stamps Paula bought.

s = 35

Got questions? Get instant answers now!

Writing exercises

Explain how you find the least common denominator of 3 8 , 1 6 , and 2 3 .

Got questions? Get instant answers now!

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?

Answers will vary.

Got questions? Get instant answers now!

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

Got questions? Get instant answers now!

In the equation 0.35 x + 2.1 = 3.85 what is the LCD? How do you know?

100. Justifications will vary.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads: “solve equations with fraction coefficients,” and “solve equations with decimal coefficients.” The rest of the cells are blank.

Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?

Questions & Answers

how did the oxygen help a human being
Achol Reply
how did the nutrition help the plants
Achol Reply
Biology is a branch of Natural science which deals/About living Organism.
Ahmedin Reply
what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
cell is the smallest unit of the humanity biologically
Abraham
what is biology
Victoria Reply
what is biology
Abraham
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask