Conquering Two-Step Inequalities

Algebra 1 Grades High School 4:32 Video
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Lesson Description

Learn how to solve two-step linear inequalities, including dealing with fractions and negative coefficients, and graph the solution set.

Video Resource

Solving a two-step inequality | Linear inequalities | Algebra I | Khan Academy

Khan Academy

Duration: 4:32
Watch on YouTube

Key Concepts

  • Inequality properties
  • Solving two-step inequalities
  • Graphing inequalities on a number line
  • Dealing with fractions and mixed numbers in inequalities

Learning Objectives

  • Students will be able to solve two-step linear inequalities.
  • Students will be able to graph the solution set of a linear inequality on a number line.
  • Students will be able to convert mixed numbers to improper fractions.
  • Students will be able to apply the multiplication/division property of inequality, remembering to flip the inequality sign when multiplying or dividing by a negative number.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic properties of inequalities: adding or subtracting the same number from both sides maintains the inequality, multiplying or dividing by a positive number maintains the inequality, and multiplying or dividing by a negative number reverses the inequality.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Solving a two-step inequality | Linear inequalities | Algebra I | Khan Academy". Instruct students to take notes on the steps demonstrated in the video.
  • Worked Example (10 mins)
    Work through the example from the video on the board, explaining each step in detail. Emphasize the importance of flipping the inequality sign when multiplying or dividing by a negative number. Also demonstrate how to change mixed numbers to improper fractions, and simplify expressions by multiplying by the common denominator.
  • Practice Problems (15 mins)
    Have students work on practice problems individually or in pairs. Provide a mix of problems, including those with fractions, mixed numbers, and negative coefficients. Circulate to assist students as needed.
  • Review and Wrap-up (5 mins)
    Review the solutions to the practice problems. Address any remaining questions or misconceptions. Summarize the key steps for solving two-step inequalities.

Interactive Exercises

  • Number Line Graphing
    Provide students with a set of inequalities and have them graph the solution sets on number lines. Use different colored markers to represent different inequalities and their solutions.
  • Inequality Card Sort
    Create a set of cards with inequalities and their corresponding solutions. Have students sort the cards to match each inequality with its correct solution.

Discussion Questions

  • Why is it important to remember to flip the inequality sign when multiplying or dividing by a negative number?
  • How does solving an inequality differ from solving an equation?
  • What are some real-world situations that can be modeled using inequalities?

Skills Developed

  • Solving linear inequalities
  • Graphing inequalities
  • Algebraic manipulation
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

Solve the inequality: 2x + 3 > 7

Correct Answer: x > 2

Question 2:

Solve the inequality: -3y - 5 ≤ 4

Correct Answer: y ≥ -3

Question 3:

Solve the inequality: (x/2) + 1 < 4

Correct Answer: x > 6

Question 4:

Solve the inequality: 5 - 2x ≥ 11

Correct Answer: x ≤ -3

Question 5:

What happens to the inequality sign when you divide both sides by a negative number?

Correct Answer: It flips

Question 6:

Solve the inequality: 4x + 6 < 2x - 2

Correct Answer: x < -4

Question 7:

Solve the inequality: -(y/3) + 2 > 5

Correct Answer: y < -9

Question 8:

Which of the following is the correct graph of x > 3 on a number line?

Correct Answer: Open circle at 3, shading to the right

Question 9:

Solve the inequality: 6 - 4x ≤ -2

Correct Answer: x ≥ 2

Question 10:

What is the first step in solving 3x - 5 > 10?

Correct Answer: Add 5 to both sides

Fill in the Blank Questions

Question 1:

To solve 5x + 2 < 12, first subtract ___ from both sides.

Correct Answer: 2

Question 2:

When multiplying or dividing both sides of an inequality by a _____ number, you must flip the inequality sign.

Correct Answer: negative

Question 3:

The solution to the inequality x - 3 > 7 is x > _____.

Correct Answer: 10

Question 4:

On a number line, x ≤ 2 is represented by a ______ circle at 2 and shading to the left.

Correct Answer: closed

Question 5:

To solve -2y > 8, divide both sides by -2, and the inequality becomes y ___ -4.

Correct Answer: <

Question 6:

The inequality 4x < -12 simplifies to x < _____.

Correct Answer: -3

Question 7:

When graphing x > -1, you use an _____ circle at -1.

Correct Answer: open

Question 8:

The solution to (x/3) > 2 is x > _____.

Correct Answer: 6

Question 9:

If 2x - 5 ≥ 1, then 2x ≥ _____.

Correct Answer: 6

Question 10:

The solution set of an inequality includes all values that _____ the inequality.

Correct Answer: satisfy

Educational Standards

A1.A.2.1:Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. A1.A.3.3:Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. A1.N.1.2:Add, subtract, multiply, divide, and simplify square roots of constants, rationalizing the denominator when necessary.

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