Solving Simple, Multi-Step Equations And Equations With Variables On Both Sides Worksheet Page 14
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40Using the Distributive Property to Solve an Equation
3 3
EXAMPLE
Solve 2(1 − 5x) + 4 = −8.
2(1 − 5x) + 4 = −8
Write the equation.
Study Tip
2(1) − 2(5x) + 4 = −8
Distributive Property
Here is another way to
2 − 10x + 4 = −8
Multiply.
solve the equation in
−10x + 6 = −8
Example 3.
Combine like terms.
2(1 − 5x) + 4 = −8
− 6
− 6
Subtraction Property of Equality
2(1 − 5x) = −12
−10x = −14
1 − 5x = −6
Simplify.
−5x = −7
−10x
−14
=
—
—
Division Property of Equality
x = 1.4
−10
−10
x = 1.4
Simplify.
4 4
Real-Life Application
EXAMPLE
Use the table to fi nd the number of miles x
Day
Miles
you need to run on Friday so that the mean
Monday
2
number of miles run per day is 1.5.
Tuesday
0
Write an equation using the defi nition of mean.
Wednesday
1.5
sum of the data
2 + 0 + 1.5 + 0 + x
Thursday
0
= 1.5
——
Write the equation.
5
Friday
x
number of values
3.5 + x
= 1.5
—
Combine like terms.
5
⋅
⋅
3.5 + x
Multiplication Property
=
—
5
5
1.5
Undo the division.
5
of Equality
3.5 + x =
7.5
Simplify.
Subtraction Property
− 3.5
− 3.5
Undo the addition.
of Equality
x = 4
Simplify.
So, you need to run 4 miles on Friday.
Solve the equation. Check your solution.
4. −3(x + 2) + 5x = −9
5 + 1.5(2d − 1) = 0.5
5.
Exercises 10 and 11
6. You scored 88, 92, and 87 on three tests. Write and solve an
equation to fi nd the score you need on the fourth test so that
your mean test score is 90.
Section 1.2
Solving Multi-Step Equations
13
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