Lesson 3: Practice Problems

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.

A hanger diagram with a red circle on the left hanging lower than the blue square on the right.

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

Here is an inequality: $- 3 x > 18$ .

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

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:

$t < m$
$m > 10$
$e > 10$
$t > 10$
$e > m$
$t < e$

Problem 5

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

$x + 3 > 70$
$x + 3 < 70$
$- 5 x < 2$
$5 x < 2$