Lesson 3

There is a closed carton of eggs in Mai's refrigerator. The carton contains \(e\) eggs and it can hold 12 eggs. 

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

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

3. What are some possible values of \(e\) that will make both \(e < 12\) and \(e > 0\) true?

Here is a diagram of an unbalanced hanger.

1. 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.
2. One red circle weighs 12 grams. Write an inequality to represent the weight of one blue square.
3. Could 0 be a value of \(s\)? Explain your reasoning.

Here is an inequality: \(\text-3x > 18\).

1. List some values for \(x\) that would make this inequality true.
2. How are the solutions to the inequality \(\text-3x \geq 18\) different from the solutions to \(\text-3x > 18\)? Explain your reasoning.

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:

\(t < j\)

\(m > 10\)

\(e > 10\)

\(t > 10\)

\(e > m\)

\(t < e\)

For each inequality, find two values for \(x\) that make the inequality true and two values that make it false.

1. \(x+3>70\)
2. \(x+3<70\)
3. \(\text-5x<2\)
4. \(5x<2\)