Reintroducing Inequalities


The number line shows values of  that make the inequality  true.

Select all the values of  from this list that make the inequality  true.

Activity #1

Inequalities Quick Review.

  • Read the statement about the sign at the amusement park below and answer the questions that follow.

A sign next to a roller coaster at an amusement park says, “You must be at least 60 inches tall to ride.” Noah is happy to know that he is tall enough to ride.

(2.) Explain how you know your answer above is correct.

(3.) Noah’s friend is 2 inches shorter than Noah. Can you tell if Noah’s friend is tall enough to go on the ride? Explain or show your reasoning.

(4.) List one possible height for Noah that means that his friend is tall enough to go on the ride.

(5.) List one possible height for Noah that means that his friend is too short for the ride.

(6.) On the number line below, show all the possible heights that Noah’s friend could be.

(7.) Noah’s friend is inches tall. Use and any of the symbols <, =, > to express this height.

Activity #2

 Determine Values That Satisfy an Inequality.

The table below shows four inequalities and four possible values for x.

  • Decide whether each value makes each inequality true.
  • Then complete the table with “true” or “false.”

Find an example of an inequality used in the real world and describe it using a number line.

Activity #3

 Find the Interval of an Inequality on a Number Line. 

Is there any limit to the number of answers we can come up with? Inequalities will have an infinite number of solutions where equations will normally only have one solution.

  • Use the tool in the applet below to locate the interval that defines the given inequality.
  • Check your answer. If necessary, use your mouse to zoom in if part of the number line goes out of the screen.

Challenge #1

(1.) Here is an inequality: -3> 18. List some values for that would make this inequality true.

(2.) How are the solutions to the inequality -3≥ 18 different from the solutions to -3> 18? Explain your reasoning.

Challenge #2

How are the solutions to the inequality different from the solutions to ? Explain your reasoning.

Challenge #3

(1.) Describe in words how to find all numbers ≥ -2 on the number line.

(2.) How is this different from finding all numbers > -2?

Quiz Time