Unlocking Equations: Solving for x in x/a = b

Mathematics Grades 7th Grade 2:23 Video
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Lesson Description

Learn how to solve one-step linear equations of the form x/a = b by using inverse operations. This lesson reinforces the concept of maintaining equality and provides a clear, step-by-step approach to isolate the variable x.

Video Resource

How to solve equations of the form x/a = b | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 2:23
Watch on YouTube

Key Concepts

  • Inverse Operations
  • Maintaining Equality
  • Isolating the Variable

Learning Objectives

  • Students will be able to identify the operation being performed on the variable in an equation of the form x/a = b.
  • Students will be able to solve for x by using the inverse operation (multiplication) on both sides of the equation.
  • 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 solving equations and the importance of maintaining balance (equality). Ask students: 'What does it mean to 'solve' an equation?' and 'What happens if you only change one side of an equation?'
  • Video Viewing (7 mins)
    Play the Khan Academy video 'How to solve equations of the form x/a = b'. Instruct students to take notes on the steps involved in solving the equations and the importance of checking the solution.
  • Guided Practice (10 mins)
    Work through a few example problems together on the board, similar to those in the video. Emphasize the steps: Identify the operation, use the inverse operation on both sides, simplify, and check the answer. Examples: x/5 = 7, x/2 = 11, x/8 = 3.
  • Independent Practice (10 mins)
    Provide students with a set of practice problems to solve individually. Circulate to provide assistance and answer questions. Problems: x/4 = 9, x/6 = 12, x/3 = 15, x/7 = 4, x/10 = 8.
  • Review and Wrap-up (3 mins)
    Review the key concepts and steps for solving equations of the form x/a = b. Ask students to share any difficulties they encountered and address any remaining questions.

Interactive Exercises

  • Equation Balance
    Use an online interactive balance scale where students can add or subtract quantities from both sides of an equation to maintain balance and solve for x.
  • Solve and Check
    Students solve an equation on a worksheet, then trade with a partner to check each other's work. The partner must verify the solution by substituting it back into the original equation.

Discussion Questions

  • Why is it important to perform the same operation on both sides of the equation?
  • What is the inverse operation of division?
  • How can you check if your solution is correct?

Skills Developed

  • Problem-solving
  • Algebraic thinking
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the inverse operation of division?

Correct Answer: Multiplication

Question 2:

To solve the equation x/4 = 8, you should...

Correct Answer: Multiply both sides by 4

Question 3:

What is the value of x in the equation x/3 = 9?

Correct Answer: 27

Question 4:

Why is it important to do the same thing to both sides of an equation?

Correct Answer: To keep the equation balanced

Question 5:

If x/5 = 10, what does x equal?

Correct Answer: 50

Question 6:

What is the first step in solving x/7 = 2?

Correct Answer: Multiply both sides by 7

Question 7:

Which of the following is equivalent to x/6 = 4?

Correct Answer: x = 4 * 6

Question 8:

In the equation x/a = b, what does 'a' represent?

Correct Answer: A number being divided into x

Question 9:

What should you do after solving an equation?

Correct Answer: Check your solution

Question 10:

Solve: x/11 = 3

Correct Answer: 33

Fill in the Blank Questions

Question 1:

To solve for x in x/a = b, you should ____________ both sides by a.

Correct Answer: multiply

Question 2:

The inverse operation of division is ____________.

Correct Answer: multiplication

Question 3:

If x/2 = 6, then x = ____________.

Correct Answer: 12

Question 4:

After solving an equation, you should always ____________ your solution.

Correct Answer: check

Question 5:

In the equation x/5 = 7, x is being ____________ by 5.

Correct Answer: divided

Question 6:

To keep an equation balanced, you must do the same thing to ____________ sides.

Correct Answer: both

Question 7:

If x/8 = 4, then multiplying both sides by 8 gives you x = ____________.

Correct Answer: 32

Question 8:

The equation x/a = b represents a ____________ relationship between x, a, and b when solving for x.

Correct Answer: linear

Question 9:

Solving for x means to ____________ the variable x.

Correct Answer: isolate

Question 10:

If x/9 = 1, then x = ____________.

Correct Answer: 9

Educational Standards

7.A.3.1:Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. 7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. 7.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

Teaching Materials

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