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

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

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 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.

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.

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.

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.

Solve 4x < 32. Explain your steps. Write your solution using set notation. Graph your solution.

Refer to the example below.

a. Explain why the Distributive Property applies first in the solution.

b. Could the properties have been applied in a different order than displayed below? If so, would this make finding the solution easier or more difficult? Discuss.

c. How would the solution change if the simplified coefficient of x were negative?

Example:

Find the solution set. Justify each step and graph your solution.

$$\begin{array}{rlrl} 3(2 x-3) & \leq x+1 & \\ 6 x-9 & \leq x+1 & & \\ 6 x \quad\quad -9 & \leq x \quad\quad& +1& \\ & \leq & & \\ 5 x-9+9 & \leq & & \text { Simplify. } \\ & \leq & & \\ & \leq & & \\ & \leq & & \text { Simplify. } \end{array}$$

Solution set: _________

How can you tell the difference between the addition and subtraction properties of inequality and the addition and subtraction properties of equality?

Karin has $3 to spend in the arcade. The game she likes costs 50 cents per play. What are the possible numbers of times that she can play? Give and solve an inequality for the situation.

A citizen should be at least 35 years old in order to run for the Presidency of the United States. Define a variable and give an inequality for this situation.

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 $\{x \mid x>\quad\}$