Chapter 12: Solving One-Step Equations

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

12.1 The Balance Scale

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:

Whatever you do to one side of the equation,
you MUST do to the other.

12.2 Inverse Operations

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 (•)

12.3 Examples in Action

Example 1: Addition

x + 8 = 20

To undo the "plus 8," we subtract 8 from both sides.

x + 8 - 8 = 20 - 8
Result: x = 12

Example 2: Multiplication

5x = 35

To undo the "times 5," we divide both sides by 5.

5x / 5 = 35 / 5
Result: x = 7

Chapter 12 Review

Solve for the variable in each equation:

  1. x - 10 = 4
  2. y + 15 = 25
  3. 3a = 21
  4. x / 4 = 5

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Doctor's Recommendation: The Law of Balance

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.

View Balance Scales on Amazon

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