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

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.

Solve the inequality, $|x|-2 \leq 3$, and graph your solution.

Solve. Explain your steps. Give the solution in set notation. Graph your solution.

$$x+1 \leq-2$$

Sariq's last four test scores in history were 87, 85, 91, and 88 . What scores on his next test will give him an average of 90 or above? Give and solve an inequality. Display your work.

Which is the next and most efficient step in solving the inequality for x?

-4x > 12

A. $\frac{-4 x}{-4}<\frac{12}{-4}$

B. $\frac{-4 x}{4}>\frac{12}{4}$

C. $\frac{-4 x}{-4}>\frac{12}{-4}$

D. $\frac{-4 x}{4}<\frac{12}{4}$

Solve the inequality, -3a + 10 < -11, and graph the solution.

Solve and write the solution in set notation. Graph your solution.

$4 x+2>14$ AND $x+6 \leq 4$