Solving Two-Step Equations
Objective Learn to solve linear equations
that involve more than one operation by using the Addition,
Subtraction, Multiplication, and Division Properties of Equality.
This material is crucial in algebra. Thus, it is beneficial
that you learn how to use these skills fluently.
Solving Two-Step Equations
Use the following examples to review the techniques for
solving one-step equations.
Example 1
Solve x + 7 = 15.
Solution
| x + 7 |
= 15 |
|
| x + 7 - 7 |
= 15 - 7 |
Subtract 7 from each side. |
| x = 8 |
|
The solution is 8. |
In this example, we used subtraction to undo the addition of
7. Thus, we used the Subtraction Property of Equality.
Example 2
Solve 3x = 27.
Solution
| 3x = 27 |
|
 |
Divide each side by 3 |
| x = 9 |
The solution is 9. |
In this example, we used division to undo the multiplication
of 3. Thus, we used the Division Property of Equality.
Sometimes, we encounter problems where there is both addition
and multiplication in the equation. We must use both of these
methods to solve these kinds of problems.
Example 3
Morgan bought a book for $10 and some CDs. The cost of each CD
was $12. If Morgan spent a total of $46, how many CDs did she
buy?
Solution
First, set up an equation. Let c represent the number of CDs
Morgan bought. Since the cost of each CD is $12, the amount
Morgan spent on CDs is given by 12c dollars. Morgan also spent
$10 on a book. So, the total amount Morgan spent is
12c + 10 dollars.
We know that Morgan spent $46. So, we can write
12c + 10 = 46.
To solve this equation, we need to isolate c on the left side
of the equation. This means we must undo the addition of 10 and
the multiplication of 12. First, undo the addition of 10. Then
undo the multiplication of 12.
| 12c + 10 |
= 46 |
|
| 12c + 10 - 10 |
= 46 - 10 |
Subtract 10 from each side. |
| 12c |
= 36 |
|
 |
 |
Divide each side by 12. |
| c |
= 3 |
|
So, Morgan bought 3 CDs.
The steps in solving two-step equations are:
(1) Undo any addition or subtraction. This leaves an equation
with only multiplication or division.
(2) Undo any multiplication or division.
Try to write and solve various two-step equations by yourself.
Be sure to include problems with negative coefficients and
constants, and some fractions.
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