Lesson 18: Practice Problems

Problem 1

Here is an inequality: $\frac{7 x + 6}{2} \leq 3 x + 2$

Select all of the values that are a solution to the inequality.

$a = - 3$
$x = - 2$
$x = - 1$
$x = 0$
$x = 1$
$x = 2$
$x = 3$

Problem 2

Find the solution set to this inequality: $2 x - 3 > \frac{2 x - 5}{2}$

$x < \frac{1}{2}$
$x > \frac{1}{2}$
$x \leq \frac{1}{2}$
$x \geq \frac{1}{2}$

Problem 3

Here is an inequality: $\frac{- 10 + x}{4} + 5 \geq \frac{7 x - 5}{3}$

What value of $x$ will produce equality (or make the two sides equal)?

Problem 4

Noah is solving the inequality $7 x + 5 > 2 x + 35$ . First, he solves the equation $7 x + 5 = 2 x + 35$ and gets $x = 6$ .

How does the solution to the equation $7 x + 5 = 2 x + 35$ help Noah solve the inequality $7 x + 5 > 2 x + 35$ ? Explain your reasoning.

Problem 5

Which graph represents the solution to $5 + 8 x < 3 (2 x + 4)$ ?

Problem 6

The principal of a school is hosting a small luncheon for her staff. She plans to prepare two sandwiches for each person. Some staff members offer to bring salads and beverages.

The principal has a budget of $225 and expects at least 16 people to attend. Sandwiches cost $3 each.

Select all of the equations and inequalities that could represent the constraints in the situation, where $n$ is number of people attending and $s$ is number of sandwiches.

$n \geq 16$
$n \geq 32$
$s < 2 n$
$s = 2 n$
$3 n \leq 225$
$3 s \leq 225$

Problem 7

Students at the college are allowed to work on campus no more than 20 hours per week. The jobs that are available pay different rates, starting from $8.75 an hour. Students can earn a maximum of $320 per week.

Write at least two inequalities that could represent the constraints in this situation. Be sure to specify what your variables represent.