Intermediate Algebra (11th edition)

124 CHAPTER 2 Linear Equations, Inequalities, and Applications

2.3 Applications of Linear Equations

Solving an Applied Problem

Step 1 Read the problem.

Step 2 Assign a variable.

Step 3 Write an equation.

Step 4 Solve the equation.

Step 5 State the answer.

Step 6 Check.

How many liters of 30% alcohol solution and 80% alcohol solution

must be mixed to obtain 100 L of 50% alcohol solution?

Let

Then 100-x=number of liters of 80% solution needed.

x=number of liters of 30% solution needed.

2.2 Formulas and Percent

Solving a Formula for a Specified Variable (Solving a
Literal Equation)

Step 1 If the equation contains fractions, multiply both
sides by the LCD to clear the fractions.

Step 2 Transform so that all terms with the specified
variable are on one side and all terms without
that variable are on the other side.

Step 3 Divide each side by the factor that is the
coefficient of the specified variable.

Solve for h.

Multiply by 2.

or h= Divide by b.

2 a

b

2 a

b

=h,

2 a=bh

2 a= 2 a

1

2

bhb

a=

1

2

bh

a=

1

2

bh

The equation is

The solution of the equation is 60. Thus, 60 L of 30% solution and

L of 80% solution are needed.

0.30 1602 +0.80 1100 - 602 = 50 is true.

100 - 60 = 40

0.30x+0.80 1100 - x 2 =0.50 11002.

Liters Percent Liters of

of Solution (as a decimal) Pure Alcohol

x 0.30 0.30x

0.80 0.80

100 0.50 0.50 11002

100 - x 1100 - x 2

2.1 Linear Equations in One Variable

Solving a Linear Equation in One Variable

Step 1 Clear fractions.

Step 2 Simplify each side separately.

Step 3 Isolate the variable terms on one side.

Step 4 Isolate the variable.

Step 5 Check.

Solve.

Distributive property

Add 12x.

Subtract 16.

Divide by 4.

The solution set is. This can be checked by substituting 4 for xin

the original equation.

546

4 =x

16

4

=

4 x

4

16 = 4 x

32 - 16 = 16 + 4 x- 16

32 = 16 + 4 x

32 - 12 x+ 12 x= 16 - 8 x+ 12 x

32 - 12 x= 16 - 8 x

32 - 12 x= 32 - 8 x- 16

418 - 3 x 2 = 32 - 81 x+ 22

QUICK REVIEW

CONCEPTS EXAMPLES

(continued)