Solutions of Inequalities


Match each story with a numberline and a description.

Activity #1

Write and Represent an Inequality on a Number Line.

Priya finds these height requirements for some of the rides at an amusement park.

  • Study the table and answer the questions below.

(1.) Write an inequality for each of the the three height requirements. Use for the unknown height.

(2.) Represent each height requirement on the number line below.

(3.) Han’s cousin is 55 inches tall. Han doesn’t think she is tall enough to ride the High Bounce, but Kiran believes that she is tall enough. Do you agree with Han or Kiran? Why?

(4.) Priya can ride the Climb-A-Thon, but she cannot ride the High Bounce or the Twirl-O-Coaster.

(5.) Priya can ride the Climb-A-Thon, but she cannot ride the High Bounce or the Twirl-O-Coaster. What could be Priya’s height? Why?

(6.) Jada is 56 inches tall. Which rides can she go on?

(7.) Kiran is 60 inches tall. Which rides can he go on?

The inequalities < 75  and  > 64 represent the height restrictions, in inches, of another ride. Write three values that are solutions to both of these inequalities.

(8.) Represent the height restrictions for all three rides on a single number line, using a different color for each ride.

Activity #2

Practice Solving Simple Linear Inequalities in One Variable.

  • To score a point, use the red slider to guess an answer to the inequality.​
  • Pull the CheckAnswer slider to the right to see the correct answer.​
  • Click the reset button to have a new question.

Activity #3

Solve One Step-Linear Inequalities.

  • Solve the inequality.
  • Choose the inequality sign by checking the appropriate box on the right.
  • Enter your value as a decimal, and press the Enter key. If your answer is right, you’ll see . Otherwise, there’d be no response.
  • Then click for a new problem. Solve as many problems as you can in this activity to master the topic.

Challenge #1

A sign on the road says: “Speed limit, 60 miles per hour.” Let S be the speed of a car.

(1.) Write an inequality that matches the information on the sign.

(2.) Draw a number line to represent the inequality above.

Could 60 be a value of S ? Explain your reasoning.

Challenge #2

Challenge #3

Quiz Time