Solving Equations
Using Addition and Subtraction
After studying this lesson, you will be able to:
- Solve equations using addition and subtraction.
A mathematical statement that contains an equal sign is called
an equation .
Steps for Solving Equations:
1. Remove parentheses by multiplying (this step is not always
necessary)
2. Collect like terms on each side of the equal sign
3. Isolate the variable by undoing the operation
4. Check by substituting the solution into the original
equation
The equal sign divides equations into 2 parts or 2 sides.
Equations are like balance scales. Whatever is done to one side,
must be done to the other side in order to maintain equality or
balance.
Example 1
| z + 6 = -9 |
There are no parentheses to be removed
and no likes terms to collect |
| z + 6 - 6 = -9 - 6 |
To isolate the variable, we
"undo" the +6 by subtracting 6 from each side |
| z = -15 |
|
Check:
substitute -15 for z in the original equation
(-15) + 6 = -9
-9 = -9
Example 2
| x - (-4) = 10 |
There are no parentheses to be removed
and no likes terms to collect |
| x + 4 = 10 |
Since there are 2 negative signs, we
"add the opposite" to avoid confusion |
| x + 4 -4 = 10 -4 |
To isolate the variable, we
"undo" the +4 by subtracting 4 from each side |
| x = 6 |
|
Check:
substitute 6 for x in the original equation
6 - (-4) = 10 (remember to "add the opposite")
10 = 10
Example 3
| p - (-2) = -2 |
There are no parentheses to be removed
and no likes terms to collect |
| p + 2 = -2 |
Since there are 2 negative signs, we add
the opposite to avoid confusion |
| p + 2 -2 = -2 -2 |
To isolate the variable, we undo the +2
by subtracting 2 from each side |
| p = -4 |
|
Check:
substitute -4 for p in the original equation
(-4) - (-2) = -2 (remember to add the opposite)
-4 + 2 = -2
-2 = -2
Example 4
| x + (-21) = 5.3 |
There are no parentheses to be removed
and no likes terms to collect |
| x + (-21) + 2.1 = 5.3 + 2.1 |
To isolate the variable, we
"undo" the -2.1 by adding 2.1 to each side |
| x = 7.4 |
|
Check:
substitute 7.4 for x in the original equation (7.4) + (-2.1) =
5.3
5.3 = 5.3
|
