Solving Two-Step Equations with Fractions

Algebra 1 Grades High School 3:04 Video
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Lesson Description

Learn how to solve two-step linear equations where the variable is in the numerator of a fraction. This lesson covers isolating the variable term and using inverse operations to find the solution.

Video Resource

Example: two-step equation with numerator x | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 3:04
Watch on YouTube

Key Concepts

  • Inverse operations (addition/subtraction, multiplication/division)
  • Properties of equality (addition, subtraction, multiplication, division)
  • Isolating a variable

Learning Objectives

  • Students will be able to isolate the term containing the variable in a two-step equation.
  • Students will be able to solve two-step linear equations with the variable in the numerator of a fraction using inverse operations.
  • Students will be able to check their solution by substituting it back into the original equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of inverse operations (addition/subtraction, multiplication/division) and their importance in solving equations. Briefly discuss the properties of equality.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Example: two-step equation with numerator x | Linear equations | Algebra I | Khan Academy'. Instruct students to pay attention to how the variable term is isolated and how inverse operations are applied.
  • Guided Practice (15 mins)
    Work through a similar example problem on the board, explaining each step in detail. Emphasize the importance of performing the same operation on both sides of the equation to maintain balance. Example: (x/3) - 5 = -10
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to solve independently. Problems should include equations with the variable in the numerator of a fraction. Examples: (x/2) + 4 = 9; -2 = (x/5) - 1; (x/-3) + 6 = -6
  • Review and Check (8 mins)
    Go through the answers to the independent practice problems. Have students explain their solution process. Address any misconceptions. Discuss the importance of checking the solution.

Interactive Exercises

  • Equation Balance
    Use an online equation balance tool where students can visually see how operations affect the balance of an equation. Students can experiment with different operations to isolate the variable.
  • Error Analysis
    Present students with an equation that has been solved incorrectly. Have them identify the error and explain how to correct it.

Discussion Questions

  • Why is it important to perform the same operation on both sides of the equation?
  • What are the inverse operations for addition, subtraction, multiplication, and division?
  • Why do we isolate the variable term first before dealing with the denominator?

Skills Developed

  • Problem-solving
  • Algebraic manipulation
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the first step in solving the equation (x/5) + 3 = 8?

Correct Answer: Subtract 3 from both sides

Question 2:

What is the inverse operation of dividing by 4?

Correct Answer: Multiplying by 4

Question 3:

Solve for x: (x/2) - 1 = 4

Correct Answer: x = 10

Question 4:

Solve for x: (x/3) + 2 = 5

Correct Answer: x = 15

Question 5:

Solve for x: -3 = (x/4) - 2

Correct Answer: x = -4

Question 6:

What should you do after you find a potential solution for x?

Correct Answer: Check it by plugging it back into the equation.

Question 7:

What is the second step in solving (x/-2) + 7 = 1?

Correct Answer: Multiply both sides by -2

Question 8:

What is the first step in solving (x/7) - 9 = 1?

Correct Answer: Add 9 to both sides

Question 9:

Solve for x: 3 = (x/-5) + 8

Correct Answer: x = -40

Question 10:

Why is it important to keep the equation balanced when solving for x?

Correct Answer: To isolate the variable without changing the value of x.

Fill in the Blank Questions

Question 1:

The goal when solving for x is to ______ the variable.

Correct Answer: isolate

Question 2:

To undo addition, you use the inverse operation of ______.

Correct Answer: subtraction

Question 3:

If you multiply one side of the equation by 3, you must also ______ the other side by 3.

Correct Answer: multiply

Question 4:

Solve for x: (x/6) + 1 = 7; x = ______

Correct Answer: 36

Question 5:

Solve for x: (x/-4) - 3 = 2; x = ______

Correct Answer: -20

Question 6:

The number located on the bottom of the fraction is called the ________.

Correct Answer: denominator

Question 7:

To check your work after solving for x, you can ______ the value back into the original equation.

Correct Answer: substitute

Question 8:

Solve for x: 9 = (x/11) + 3; x = ______

Correct Answer: 66

Question 9:

Solve for x: (x/8) - 4 = 1; x = ______

Correct Answer: 40

Question 10:

Adding or subtracting the same number from both sides of an equation is called the _______ property of equality.

Correct Answer: addition/subtraction

Educational Standards

A1.A.1:Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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