Creating and Solving Inequalities

Creating and Solving Linear Inequalities

​8.PAR.3.3 Create and solve linear equations and inequalities in one variable within a relevant, real-life application.

8.PAR.3.4 Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.

8.PAR.3.5 Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.

Review from Last Week.......

Answer the next question with your group

Multiple Choice

There were approximately 11,000 students enrolled at Western Carolina last year. If this figure goes up by about 225 students each year, how many years will it take the enrollment to reach 20,000 students?

• 10 years

• 20 years

• 30 years

• 40 years

Turn and Talk
(1 minute)

​What is the difference between an equation and an inequality?

Turn and Talk
(Equation vs Inequality)

An EQUATION shows the EQUAL value of TWO expressions. An equation has ONE solution, NO solution, or INFINITELY MANY solutions.

An INEQUALITY shows that an expression is LESSER THAN or MORE THAN the other. An inequality has MORE THAN one solution.

​When graphing inequalities:

GREATER THAN or LESS THAN has an OPEN circle.

Greater than or EQUAL TO or Less than or EQUAL TO has a CLOSED circle.

Multiple Choice

Which graph represents the following inequality:

$$x\ <\ 5$$

Multiple Choice

Which inequality matches the graph.

• $$x\ <-4.5$$

• $$x\ >-4.5$$

• $$x\ \le-4.5$$

• $$x\ge-4.5$$

​One-Step Inequalities
(Add or Subtract)

• ​ADD or SUBTRACT to ISOLATE the variable.

• SOLVE by performing the INVERSE operation.

​One-Step Inequalities
(Multiply or Divide-Positive Sign)

• ​MULTIPLY or DIVIDE to ISOLATE the variable.

• SOLVE by performing the INVERSE operation.

• SIMPLIFY your answer.

​One-Step Inequalities
(Multiply or Divide-Negative Sign)

• ​MULTIPLY or DIVIDE to ISOLATE the variable.

• SOLVE by performing the INVERSE operation.

• When MULTIPLYING or DIVIDING by a NEGATIVE number, FLIP the inequality sign.

• SIMPLIFY your answer.

​Two-Step Inequalities

• Step 1: ADD or SUBTRACT the CONSTANT on the side with the variable.

• Step 2: ​MULTIPLY or DIVIDE to ISOLATE the variable.

• If MULTIPLYING or DIVIDING by a NEGATIVE number, FLIP the inequality sign.

Multiple Choice

Solve the following inequality:

$$3t\ -\ 12\ \le\ -9$$

• $$t\ \ge1$$

• $$t\le1$$

• $$t\ge7$$

• $$t\le7$$

Multiple Choice

Solve the following inequality:

$$4\ -\ 2y\ <\ 12$$

• $$y\ >-4$$

• $$y<-4$$

• $$y>-8$$

• $$y<-8$$

Strategies for Solving
Real World Inequality Word Problems

• ​READ through the entire problem.

• HIGHLIGHT the important information and KEY words that you need to solve the problem.

• Identify your VARIABLES.

• TRANSLATE your key words and write the INEQUALITY.

• SOLVE the problem.

Multiple Choice

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• $$200+25x\ge500$$

• $$500+25x\ge200$$

• $$500-25x\ge200$$

• $$500-25x\le200$$

Multiple Choice

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the maximum amount of hours she will need to babysit in order for her to buy her calculator?

• $$5x+10\le100$$

• $$5x-100\ge10$$

• $$10x+5\le100$$

• $$5x+10\ge100$$

​​Group Work:
Practice Problems

Multiple Select

Jim paid a gym membership fee of $50, plus $20 per month.  Jim's budget is $300, how long can he be a member at the gym?

(Select all that apply)

• 9 months

• 1 year

• 1.25 years

• 1.5 years

Multiple Choice

Penelope is going to be a vendor at the carnival. She spent $125 for the ingredients for cotton candy and candy apples and $160 for the cases of apples. She's going to sell each item for $6. How many bags of cotton candy and candy apples must she sell to make a profit?

• 58

• 59

• 47

• 48

Multiple Choice

Mrs. Scott decided that she would spend at least $150 to buy a jacket and a skirt. If the price of the jacket was $30 more than 3 times the price of the skirt, which inequality represents the lowest possible price of the skirt?

• $$s\ge60$$

• $$s\le\text{}60$$

• $$s\ge40$$

• $$s\le\text{}40$$

Multiple Choice

The dance committee hired a DJ for the spring dance. The DJ charges $125 per hour in addition to $75 for the set-up fee. The committee wants to keep the total cost under $450. Which is the maximum amount of hours the DJ will play at the dance?

• 4 hours

• 2 hours,

  59 minutes

• 3 hours, 45 minutes

• 3 hours

Poll

As a group, rate your understanding of Creating and Solving Linear Inequalities after completing this lesson:

• 4 - We understand how to create and solve linear inequalities and teach a peer how to do it.

• 3 - We understand how to create and solve linear inequalities.

• 2 - We understand how to create and solve linear inequalities with the help of our group.

• 1 - We need more help on how to create and solve linear inequalities.