Lesson 19: Practice Problems

Problem 1

Solve $2 x < 10$ . Explain how to find the solution set.

Problem 2

Lin is solving the inequality $15 - x < 14$ . She knows the solution to the equation $15 - x = 14$ is $x = 1$ .

How can Lin determine whether $x > 1$ or $x < 1$ is the solution to the inequality?

Problem 3

A cell phone company offers two texting plans. People who use plan A pay 10 cents for each text sent or received. People who use plan B pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received.

Write an inequality to represent the fact that it is cheaper for someone to use plan A than plan B. Use $x$ to represent the number of texts they send.
Solve the inequality.

Problem 4

Clare made an error when solving $- 4 x + 3 < 23$ .

$\begin{aligned} - 4 x + 3 & < 23 \\ - 4 x & < 20 \\ x & < - 5 \end{aligned}$

Describe the error that she made.

Problem 5

Diego’s goal is to walk more than 70,000 steps this week. The mean number of steps that Diego walked during the first 4 days of this week is 8,019.

Write an inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps. Remember to define any variables that you use.
If the mean number of steps Diego walks during the last 3 days of the week is 12,642, will Diego reach his goal of walking more that 70,000 steps this week?

Problem 6

What is the solution set of the inequality $\frac{x + 2}{2} \geq - 7 - \frac{x}{x}$ ?

$x \leq - 8$
$x \geq - 8$
$x \geq - \frac{9}{2}$
$x \geq 8$