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
| x + 16 = - 7 |
There are no parentheses to be removed
and no like terms to collect |
| x + 16 -16 = - 7 - 16 |
To isolate the variable, we undo the +16
by subtracting 16 from each side |
| x = -23 |
The 16 s cancel out and when you add -7
and -16 you get -23 |
Check:
substitute -23 for x in the original equation
(-23) + 16 = -7
-7 = -7 (always be sure the 2 sides are equal)
Example 2
| a + (-11) = - 4 |
There are no parentheses to be removed
and no likes terms to collect |
| a + (-11) + 11 = - 4 + 11 |
To isolate the variable, we undo the 11
by adding 11 to each side |
| a = 7 |
The 11s cancel and when you add 4 and 11
you get 7 |
Check:
substitute 7 for a in the original equation (7) + (-11) = -4
-4 = -4 (always be sure the 2 sides are equal)
Example 3
| -8 -x = 10 |
There are no parentheses to be removed
and no likes terms to collect |
| -8 + 8 -x = 10 + 8 |
To isolate the variable, we undo the 8 by
adding 8 to each side |
| -y = 18 |
This solves the equation for negative y,
but we want positive y |
| y = -18 |
Take the opposite of each side |
Check:
substitute -18 for y in the original equation
-8 (-18) = 10 (remember to add the opposite here)
10 = 10
Example 4
| -5 - y = 13 |
There are no parentheses to be removed
and no likes terms to collect |
| -5 - y + 5 = 13 + 5 |
To isolate the variable, we
"undo" the -5 by adding 5 to each side |
| -y = 18 |
This solves the equation for negative y, 4 but we
want positive y |
| y = -18 |
Take the opposite of each side |
Check:
substitute -18 for y in the original equation
-5 - (-18) = 13 (remember to "add the opposite"
here)
13 = 13
Example 5
| x + 15 = -6 |
There are no parentheses to be removed
and no likes terms to collect |
| x + 15 - 15 = -6 - 15 |
To isolate the variable, we undo the +15
by subtracting 15 from each side |
| x = -21 |
|
Check:
substitute -21 for x in the original equation
(-21) + 15 = -6
-6 = -6
|
