Algebra Class: Two-Step Equations

Solving Two-Step Equations

• A two-step equation is an algebraic equation that requires two steps to solve for the variable.
• The objective is to isolate the variable on one side of the equation using inverse operations.

Identifying Two-Step Equations

• Equations with variables that have two operations performed on them.
• Usually, the variable is added to or subtracted from a number, and then multiplied or divided by another number.

Steps to Solve a Two-Step Equation

• Step 1: Undo addition or subtraction: Add or subtract the constant number (the term that does not contain the variable) from both sides of the equation to isolate the term containing the variable.
• Step 2: Undo multiplication or division: If the variable is multiplied or divided by a number, multiply or divide both sides of the equation by that number to solve for the variable.

Examples and Explanations

• Example 1: Solve 2x + 5 = 11

• Subtract 5 from both sides: 2x + 5 - 5 = 11 - 5

• Simplifies to: 2x = 6

• Divide both sides by 2: 2x / 2 = 6 / 2

• Solution: x = 3

• Example 2: Solve 3x - 7 = 8

• Add 7 to both sides: 3x - 7 + 7 = 8 + 7

• Simplifies to: 3x = 15

• Divide both sides by 3: 3x / 3 = 15 / 3

• Solution: x = 5

• Example 3: Solve (x / 4) + 2 = 5

• Subtract 2 from both sides: (x / 4) + 2 - 2 = 5 - 2

• Simplifies to: (x / 4) = 3

• Multiply both sides by 4: (x / 4) * 4 = 3 * 4

• Solution: x = 12

Common Errors and How to Avoid Them

• Forgetting the order of operations: Remember to follow the order of operations (PEMDAS/BODMAS) when solving equations; doing addition and subtraction first, then multiplication and division.
• Making arithmetic errors: Carefully check your addition, subtraction, multiplication, and division calculations. Using a calculator can greatly assist in removing this error source.
• Incorrectly applying inverse operations: Ensure you are using inverse operations appropriately; adding to undo subtraction, and vice-versa and multiplying to undo division, and vice-versa.

Applications of Two-Step Equations

• Word Problems: Two-step equations are commonly used to solve word problems involving a combination of addition/subtraction and multiplication/division operations.
• Real-world scenarios: Many real-world problems can be modeled using two-step equations. For example, determining the number of items based on a known total and a given price per item.

Practice Problems

• Solve 5y - 2 = 13
• Solve (x / 3) + 6 = 9
• Solve 2a + 1 = 7

Key Concepts Summary

• Two-step equations involve two mathematical operations (usually addition/subtraction and multiplication/division).
• By applying inverse operations, the variable can be isolated to find its value.
• Following the correct order of operations is crucial for accuracy.