Intermediate Algebra (11th edition)

Some equations have decimal coefficients. We can clear these decimals by multi-

plying by a power of 10, such as

and so on.

This allows us to obtain integer coefficients.

Solving a Linear Equation with Decimals

Solve

Because each decimal number is given in hundredths, multiply each side of the

equation by 100. A number can be multiplied by 100 by moving the decimal point

two places to the right.

Multiply each term by 100.

Distributive property

Combine like terms and multiply.

Subtract 135.

Combine like terms.

Divide by.

x= 10

- 3

- 3 x

- 3

=

- 30

- 3

- 3 x=- 30

- 3 x+ 135 - 135 = 105 - 135

- 3 x+ 135 = 105

6 x+ 91152 - 9 x= 71152

6 x+ 9115 - x 2 = 71152

0. 06 x+ 0. 09115 - x 2 = 0. 071152

0.06x+0.09 115 - x 2 = 0.07 1152

0.06x+0.09 115 - x 2 = 0.07 1152.

EXAMPLE 5

101 = 10, 102 =100,

52 CHAPTER 2 Linear Equations, Inequalities, and Applications

Move decimal

points 2 places

to the right.

NOW TRY
EXERCISE 5
Solve.

=0.03 1 x- 52

0.08x-0.12 1 x- 42

NOW TRY ANSWER

5. 596

CHECK

Let

Multiply and subtract.

Multiply.

✓ True

The solution set is NOW TRY

NOTE Because of space limitations, we will not always show the check when solv-

ing an equation. To be sure that your solution is correct, you should always check

your work.

OBJECTIVE 6 Identify conditional equations, contradictions, and identities.

In Examples 2 – 5,all of the equations had solution sets containing oneelement, such

as in Example 5.Some equations, however, have no solutions, while others

have an infinite number of solutions. The table on the next page gives the names of

these types of equations.

5106

5106.

1.05= 1.05

0.6+0.451.05

0.6+ 0.09 152 1.05

0.06 1102 +0.09 115 - 102 0.07 1152 x=10.

0.06x+0.09 115 - x 2 = 0.07 1152