Solving Equations
2-Step Equation
After studying this lesson, you will be able to:
- Solve equations that require two steps.
Review of 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
(do this until the variable is by itself)
- "undo" addition and subtraction first
- next, "undo" multiplication and division
4. Check by substituting the solution into the original
equation
Example 1
| 3x + 4 = 10 |
This equation will require 2 steps to
solve it |
| 3x + 4 -4 = 10 -4 |
First, we need to "undo" +4 so
we subtract 4 from each side. This gives us 3x = 6
|
 |
Now, we need to "undo" 3 times
x, so we divide each side by 3 |
| x = 2 |
Now, we have the solution |
Check:
substitute 2 for x in the original equation
3 (2) + 4 = 10
6 + 4 = 10
10 = 10 (notice that it also required 2 steps to check)
Example 2
| -2x - 6 = 12 |
This equation will require 2 steps to
solve it |
| -2x - 6 + 6 = 12 + 6 |
First, we need to "undo" -6 so
we add 6 to each side This gives us -2x = 18
|
 |
Now, we need to "undo" -2 times
x, so we divide each side by -2 |
| x = -9 |
Now, we have the solution |
Check: substitute -9 for x in the original equation
-2 (-9) -6 = 12
18 - 6 = 12
12 = 12
Example 3
 |
This equation will require 2 steps to
solve it |
 |
First, we need to "undo" +9 so
we subtract 6 from each side This gives us
|
 |
Now, we need to "undo" (which
is x divided by 4), so we multiply each each side by 4.
|
| x = -12 |
Now, we have the solution |
Check:
substitute -12 for x in the original equation
-3 + 9 = 6
6 = 6
Example 4
|
