Adapted from Wentworth's Elementary Algebra for MathDoctor.net
An equation is a statement that two things are equal. If you add 5 pounds to the left side of a scale, you must add 5 pounds to the right side to keep it level. This leads us to the most important rule in all of math:
To "solve" for x, you have to undo whatever is being done to it. We use Opposites (Inverses) to cancel out numbers.
| If you see... | Use the Inverse... |
|---|---|
| Addition (+) | Subtraction (-) |
| Subtraction (-) | Addition (+) |
| Multiplication (•) | Division (/) |
| Division (/) | Multiplication (•) |
x + 8 = 20
To undo the "plus 8," we subtract 8 from both sides.
x + 8 - 8 = 20 - 8
Result: x = 12
5x = 35
To undo the "times 5," we divide both sides by 5.
5x / 5 = 35 / 5
Result: x = 7
Solve for the variable in each equation:
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An equation is a scale. In Chapter 12, we learn that adding to one side requires adding to the other. A Small Balance Scale on your desk is more than a toy—it’s a physical reminder of the "Golden Rule" of Algebra that will guide you through the rest of this course.
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