Algebra 101 - Unit 2

Solving One-Step Equations

One-step equations are the simplest type of algebraic equations. They can be solved in **just one step** by using the opposite operation to isolate the variable.

1. Steps to Solve One-Step Equations

1. Identify the variable and the operation being applied (addition, subtraction, multiplication, or division).
2. Use the opposite operation to isolate the variable.
3. Perform the operation on both sides of the equation to maintain equality.
4. Check your solution by substituting it back into the original equation.

2. Solving One-Step Equations by Addition

Use subtraction to undo addition:

• Example: x + 7 = 12
1. Subtract 7 from both sides: x + 7 - 7 = 12 - 7
2. Simplify: x = 5

3. Solving One-Step Equations by Subtraction

Use addition to undo subtraction:

• Example: y - 4 = 10
1. Add 4 to both sides: y - 4 + 4 = 10 + 4
2. Simplify: y = 14

4. Solving One-Step Equations by Multiplication

Use division to undo multiplication:

• Example: 3x = 15
1. Divide both sides by 3: 3x / 3 = 15 / 3
2. Simplify: x = 5

5. Solving One-Step Equations by Division

Use multiplication to undo division:

• Example: z / 6 = 4
1. Multiply both sides by 6: (z / 6) × 6 = 4 × 6
2. Simplify: z = 24

6. Tips for Success

• Always perform the same operation on both sides of the equation.
• Remember the “opposite operation” rule: addition ↔ subtraction, multiplication ↔ division.
• Check your answer by substituting it back into the original equation.
• Write each step clearly to avoid mistakes.

Mastering one-step equations is the foundation for solving more complex equations and inequalities in algebra.