Sam can spend no more than $75 on school supplies. He has to spend$12 on paper and pencils. Determine the maximum amount Sam can spend on a graphing calculator. Define a variable and give an inequality.

Indicate whether the value, $b=5 ; 60-10 b \leq 20$, is a solution to the inequality. Discuss.

Solve the compound inequality, $2 s+3 \leq 7$ OR 3s + 5 > 26 and graph your solution.

Indicate whether the value, m = 12; 5m + 4 > 50, is a solution to the inequality. Discuss.

Solve the inequality, $3(x+4) \leq 3 x$.

What is the solution set of the inequality 3n > - 6?

F. All real numbers less than 2 .

G. All real numbers less than -2.

H. All real numbers greater than 2 .

J. All real numbers greater than -2.

The temperature at noon in Los Angeles on a summer day was $88^{\circ} \mathrm{F}$. During the day, the temperature varied from this by as much as $7.5^{\circ} \mathrm{F}$. Give and solve an absolute-value inequality to determine the range of possible temperatures for that day.

A teacher buys a 128-ounce bottle of juice and serves it in 5-ounce cups. What are the possible numbers of cups she can fill? Give and solve an inequality.

The sum of the lengths of any two sides of a triangle should be greater than the length of the third side. What are the possible values of x for this triangle, if the sides of the triangle are (3x)cm, 40 cm, and (x +5) cm? Give and solve an inequality for the problem.

The minimum wage in the U.S. was $0.75 per hour in 1955. Define a variable and give an inequality.

Determine the solution set. Explain each step and graph your solution.

21 x + 28 < 10 - 3x

a. When solving inequalities, if you multiply by a negative number, you should _______.

b. When solving inequalities, if you divide by a negative number, you should _______.

Refer to the example below.

a. Why is the solution set the empty set in Part C?

b. Why is the solution set $\{x \mid x>1\}$ in Part D?

Example:

Solve. Write the solution in set notation. Graph the solution.

C.

$$\text { C } \begin{array}{rlrl} 2 x-3 & >3 \text { AND } x+4 & \leq 1 \\ 2 x & >6 & x & \leq-3 \\ x & >3 & \end{array}$$

Solution set: $\{x \mid x>\quad\} \cap\{x \mid x \leq \quad\}$ or the ________ set or

D.

$$\begin{aligned} & \text {} 3 x-1>2 \text { OR } 2 x+2 \geq 8 \\ & 3 x>3 \quad 2 x \geq 6 \\ & x>1 \quad x \geq 3 \\ & \end{aligned}$$

Solution set: $\{x \mid x>\quad\} \cup\{x \mid x \geq \quad\}$ or $\{x \mid x>\quad\}$

The Mexican Tetra is a tropical fish that needs a water temperature between 68 and 77 degrees Fahrenheit, inclusive. An aquarium is heated 8 degrees so that a Tetra can live in it. What temperatures could the water have been before the heating? Give and solve an inequality for the situation.