Podcast
Questions and Answers
Which of the following is NOT a two-step equation?
Which of the following is NOT a two-step equation?
- x + 2 = 5 (correct)
- 3y - 4 = 10
- 2x + 5 = 11
- 4z - 1 = 7
Solve for x: 5x - 3 = 12.
Solve for x: 5x - 3 = 12.
- x = 7
- x = 5
- x = 2
- x = 3 (correct)
What is the first step in solving the equation (y/3) + 5 = 8?
What is the first step in solving the equation (y/3) + 5 = 8?
- Add 5 to both sides
- Multiply both sides by 3
- Divide both sides by 3
- Subtract 5 from both sides (correct)
Which of the following is the correct solution to the equation -2x + 7 = 1?
Which of the following is the correct solution to the equation -2x + 7 = 1?
What is the correct order of operations for solving a two-step equation?
What is the correct order of operations for solving a two-step equation?
A store sells apples for $1.50 each and oranges for $0.75 each. Sarah bought 3 apples and some oranges, spending a total of $7.50. How many oranges did she buy?
A store sells apples for $1.50 each and oranges for $0.75 each. Sarah bought 3 apples and some oranges, spending a total of $7.50. How many oranges did she buy?
Which of the following is NOT a step in solving the equation 3x - 5 = 10?
Which of the following is NOT a step in solving the equation 3x - 5 = 10?
What is the inverse operation of multiplying by 4?
What is the inverse operation of multiplying by 4?
Flashcards
Two-Step Equations
Two-Step Equations
Algebraic equations needing two steps to solve for a variable.
Inverse Operations
Inverse Operations
Operations that undo each other, aiding in isolating variables.
Solving Steps
Solving Steps
The process of first undoing addition/subtraction, then multiplication/division to isolate a variable.
Addition Property of Equality
Addition Property of Equality
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Subtraction Property of Equality
Subtraction Property of Equality
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Common Mistakes
Common Mistakes
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Checking Solutions
Checking Solutions
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Word Problems
Word Problems
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Study Notes
Understanding Two-Step Equations
- Two-step equations are algebraic equations that require two steps to solve for the variable.
- They involve a combination of addition/subtraction and multiplication/division operations.
- The goal is to isolate the variable on one side of the equation.
Identifying Two-Step Equations
- An equation is a two-step equation if it contains a variable, and at least two operations are performed on the variable to isolate it.
Solving Two-Step Equations
- Step 1: Undo addition or subtraction: Add or subtract the constant term from both sides of the equation to isolate the term with the variable.
- Step 2: Undo multiplication or division: Divide or multiply both sides of the equation by the coefficient of the variable.
- Example: Solve 2x + 5 = 11
- Subtract 5 from both sides: 2x = 6
- Divide both sides by 2: x = 3
Key Concepts
- Inverse Operations: The operations used to isolate the variable are inverse operations—they "undo" each other.
- Properties of Equality: The following properties are crucial for solving equations:
- Addition Property of Equality: If a = b, then a + c = b + c.
- Subtraction Property of Equality: If a = b, then a - c = b – c.
- Multiplication Property of Equality: If a = b, then a * c = b * c.
- Division Property of Equality: If a = b, then a / c = b / c (assuming c ≠0).
- Checking Solutions: Substitute the solution into the original equation to verify it is correct.
Common Mistakes
- Forgetting the order of operations.
- Incorrect applying inverse operations.
- Making errors with signs, especially when subtracting negative numbers.
- Dividing or multiplying both sides by zero, which is an invalid operation.
Examples of Different Types of Two-Step Equations
- Subtraction and multiplication: 3x - 7 = 8
- Add 7 to both sides: 3x = 15
- Divide both sides by 3: x = 5.
- Addition and division: (y/4) + 2 = 6
- Subtract 2 from both sides: (y/4) = 4
- Multiply both sides by 4: y = 16.
- Negative Coefficients: -2x + 9 = 1
- Subtract 9 from both sides: −2x = −8
- Divide both sides by (−2): x = 4.
- Fractions: (x/3) + 4 = 7
- Subtract 4 from both sides: (x/3) = 3.
- Multiply both sides by 3: x = 9.
Word Problems Involving Two-Step Equations
- Translate word problems into algebraic equations.
- Identify the unknown quantities and assign variables.
- Solve the two-step equation to find the unknown values.
Practice Problems:
- Solve 5x − 2 = 13
- Solve 11 + 2y/3 = 7
- A pizza costs $15. If this includes the cost of additional toppings ($4), what is the base price of the pizza? Equation: x + 4 = 15. Solution: x = $11.
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