Lesson 10
Interpreting Inequalities
Let’s examine what inequalities can tell us.
Problem 1
There is a closed carton of eggs in Mai's refrigerator. The carton contains \(e\) eggs and it can hold 12 eggs.

What does the inequality \(e < 12\) mean in this context?

What does the inequality \(e > 0\) mean in this context?

What are some possible values of \(e\) that will make both \(e < 12\) and \(e > 0\) true?
Problem 2
Here is a diagram of an unbalanced hanger.
 Write an inequality to represent the relationship of the weights. Use \(s\) to represent the weight of the square in grams and \(c\) to represent the weight of the circle in grams.
 One red circle weighs 12 grams. Write an inequality to represent the weight of one blue square.
 Could 0 be a value of \(s\)? Explain your reasoning.
Problem 3

Jada is taller than Diego. Diego is 54 inches tall (4 feet, 6 inches). Write an inequality that compares Jada’s height in inches, \(j\), to Diego’s height.

Jada is shorter than Elena. Elena is 5 feet tall. Write an inequality that compares Jada’s height in inches, \(j\), to Elena’s height.
Problem 4
Tyler has more than $10. Elena has more money than Tyler. Mai has more money than Elena. Let \(t\) be the amount of money that Tyler has, let \(e\) be the amount of money that Elena has, and let \(m\) be the amount of money that Mai has. Select all statements that are true:
\(t < j\)
\(m > 10\)
\(e > 10\)
\(t > 10\)
\(e > m\)
\(t < e\)
Problem 5
Which is greater, \(\frac {\text{}9}{20}\) or 0.5? Explain how you know. If you get stuck, consider plotting the numbers on a number line.
Problem 6
Select all the expressions that are equivalent to \(\left(\frac{1}{2}\right)^3\).
\(\frac{1}{2} \boldcdot \frac{1}{2} \boldcdot \frac{1}{2}\)
\(\frac{1}{2^3}\)
\(\left(\frac{1}{3}\right)^2\)
\(\frac{1}{6}\)
\(\frac{1}{8}\)