3.6
Solving Decimal Equations
Goals p Find exact and approximate solutions of equations that
contain decimals.
p Solve real-life problems that use decimals.
VOCABULARY
Round-off error Round-off error is the error produced when a
decimal result is rounded in order to provide a meaningful
answer.
Example 1
Rounding for the Final Answer
Solve !48x " 31 # 124. Round to the nearest hundredth.
!48x " 31 # 124
!48x # 93
Write original equation.
Subtract 31 from each side.
93
x # $$
!48
Divide each side by !48 .
x # !1.9375
Use a calculator.
x ≈ !1.94
Round to nearest hundredth.
Answer The solution is approximately !1.94 .
Check When you substitute a rounded answer into the original
equation, the two sides of the equation may not be exactly equal,
but they should be almost equal.
!48x " 31 # 124
!48( !1.94 ) " 31 ! 124
124.12 ≈ 124
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Algebra 1 Notetaking Guide • Chapter 3
Write original equation.
Substitute !1.94 for x.
Is the answer reasonable? yes
Original Equation Involving Decimals
Example 2
Solve 2.53x ! 60.17 " 0.38x # 5.48. Round to the nearest
hundredth.
Use the same methods you learned for solving equations without
decimals.
2.53x ! 60.17 " 0.38x # 5.48
2.15x ! 60.17 " 5.48
Write original equation.
Subtract 0.38x from each
side.
2.15x " 65.65
Add 60.17 to each side.
65.65
x " $$
2.15
Divide each side by 2.15 .
x ≈ 30.53488372
Use a calculator.
x ≈ 30.53
Round to nearest hundredth.
Answer The solution is approximately 30.53 . Check this in the
original equation.
Checkpoint Solve the equation. Round to the nearest
hundredth.
1. 11x ! 5 " 26
2.82
2. 23 ! 6y " 7
2.67
3. !48 " 13n # 14
!4.77
4. 6.26x ! 54.89 " 0.86x # 9.76
11.97
5. 12.78 # 2.75x " 5.26 # 7.23x
1.68
Lesson 3.6 • Algebra 1 Notetaking Guide
59
Example 3
Changing Decimal Coefficients to Integers
Solve 3.7 ! 8.4x " 1.2x # 35.9. Round to the nearest tenth.
Solution
Because the
coefficients and
constant terms each
have only one
decimal place, you
can rewrite the
equation without
decimals by
multiplying each
side by 10.
Write original equation.
3.7 ! 8.4x " 1.2x # 35.9
Multiply each side by 10.
37 ! 84x " 12x # 359
37 " 96x # 359
Add 84x to each side.
!322 " 96x
Subtract 359 from each side.
!322
$$ " x
96
Divide each side by 96 .
!3.354166667 ≈ x
!3.4 ≈ x
Use a calculator.
Round to nearest tenth.
Answer The solution is approximately !3.4 . Check this in the
original equation.
Checkpoint Multiply the equation by a power of 10 to write an
equivalent equation with integer coefficients.
6. 7.2x # 1.3 " 3.8 # 4.2x
72x # 13 " 38 # 42x
7. 0.97y ! 0.29 " 0.83y
97y ! 29 " 83y
Solve the equation. Round to the nearest hundredth.
8. 37.2x # 95.2 " 79.9x
2.23
9. 56.44y # 28.03 "
75.67y ! 81.97
5.72
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Algebra 1 Notetaking Guide • Chapter 3