Step 2 Subtract 7.
Combine like terms.Step 3 Divide by.
Step 4 Check to confirm that 5 - 26 is the solution set. NOW TRY
x=- 2
- 4
- 4 x
- 4
=
8
- 4
- 4 x= 8
- 4 x+ 7 - 7 = 15 - 7
102 CHAPTER 2 Linear Equations and Inequalities in One Variable
Solving an Equation with Decimals as CoefficientsSolve
Step 1 The decimals here are expressed as tenths and hundredths and
. We choose the least exponent on 10 needed to eliminate the decimals.
Here, we use.
Multiply by 100.
Distributive property
Multiply.
Distributive property
Multiply.
Combine like terms.Step 2 Subtract 100.
Combine like terms.Step 3 Divide by 5.
Step 4 Check to confirm that 5166 is the solution set. NOW TRY
t= 16
5 t
5
=
80
5
5 t= 80
5 t+ 100 - 100 = 180 - 100
5 t+ 100 = 180
10 t+ 100 - 5 t= 180
10 t+ 5 1202 + 5 1 - t 2 = 180
10 t+ 5 120 - t 2 = 9 1202
100 1 0.10t 2 + 100 3 0.05 120 - t 24 = 100 3 0.09 12024
100 3 0.10t+ 0.05 120 - t 24 = 100 3 0.09 12024
0.10t+ 0.05 120 - t 2 =0.09 1202 0.1=0.10
0.1t+ 0.05 120 - t 2 =0.09 1202
10 2 = 100
0.09 2
1 0.1 2 1 0.05
0.1t+0.05 120 - t 2 =0.09 1202.
EXAMPLE 8
CAUTION Be sure you understand how to multiply by the LCD to clear an
equation of fractions. Study Step 1 in Examples 6 and 7 carefully.
NOTE In Example 8,multiplying by 100 is the same as moving the decimal point
two places to the right.
10 t+ 5 120 - t 2 = 9 1202 Multiply by 100.
0 .10t+ 0 .05 120 - t 2 = 0 .09 1202
OBJECTIVE 3 Solve equations with no solution or infinitely many
solutions.Each equation so far has had exactly one solution. An equation with
exactly one solution is a conditional equationbecause it is only true under certain
conditions. Some equations may have no solution or infinitely many solutions.
NOW TRY
EXERCISE 8
Solve.
0.05 113 - t 2 - 0.2t=0.08 1302
NOW TRY ANSWERS
- 546 8. 5 - 76
NOW TRY
EXERCISE 7
Solve.
2
31 x+ 22 -1
2
13 x+ 42 =- 4http://www.ebook777.com
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