Inequalities Today you will learn to: graph and write inequalities solve inequalities by using properties of inequality M07.B-E.2.2.2: Solve word problems leading to inequalities of the px + q > r or px + q < r, where p, q, and r are rational numbers, and graph the solution set of the inequality.

Warm-up Problem: Inequalities Your elementary school is having a fall carnival. Admission into the carnival is $3 and each game inside the carnival costs $1. Write an inequality that represents the possible number of games that can be played having $10. What is the maximum number of games that can be played?

What are Inequalities? A mathematical sentence that contains, ≤, ≥, or ≠ is an inequality. Sometimes (and especially in this class), an inequality contains a variable, such as x ≥ 2. A solution of an inequality is any value that makes the inequality true. The solution of an inequality can include many numbers. For example, 6, 8, and 15 are all solutions of x ≥ 2, because 6 ≥ 2, 8 ≥ 2, and 15 ≥ 2. Example: Which number(s) is a solution to x ≥ 5: -3, 0, 2, 5, 7.

Graphing Inequalities A graph can show all of the numbers in a solution. For x ≥ 2: Note: closed circles are used for ≤ and ≥, and open circles are used for. You can also write an inequality by analyzing its graph. Look at the number line below. What inequality is represented by the number line?

Solve Inequalities Solving inequalities means finding values for the variable that make the inequality true. The only difference between solving inequalities and solving equations is that equations have an ‘equals’ sign, where inequalities do not. You can solve inequalities using properties similar to those you used when solving equations. Just like algebraic equations, you will be using inverse operations to solve inequalities. Consider the following: x + 2 < 3 x + 2 – 2 < 3 – 2 (Subtract 2 from both sides) x < 1 This means that any value less than (but not equal to) 1 will make the inequality true!

Solve Inequalities: Examples Solve the following inequalities. A. 15x + 7 ≥ -53 B. 6d – 11 < 7 A. 9(y – 3) ≤ 36 B. 10 > 8(s – ¾)