An inequality is a mathematical sentence that contains the following symbols: . < , >, is less than or equal to is greater than or equal to is less than is greater than < > A solution to an inequality is any number that makes it true. Inequalities have many solutions. Solutions are shown by shading a number line.

Graph each inequality solution on a number line: The open circle means the 1 is not included in the solution. A. x < 1 -4 -3 -2 -1 0 1 2 3 4 The solution is all numbers less than 1. The closed circle means the −2 is included in the solution. B. -4 -3 -2 -1 0 1 2 3 4 The solution is all numbers greater than or equal to −2.

Solve this inequality and graph the solution. x + 5 < 7 − 5 − 5 To solve an inequality, follow the same steps you use to solve an equation. Solve this inequality and graph the solution. x + 5 < 7 − 5 − 5 Graph: x < 2 -4 -3 -2 -1 0 1 2 3 4 The solution is all numbers less than 2. Check: Try 1, a number less than 2. x 1 + 5 < 7 6 < 7 This sentence is true.

Solve this inequality and graph the solution. x − 3 − 5 Graph: + 3 + 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 x −2 The solution is all numbers greater than or equal to −2. Check: Try −1, a number greater than −2. −1 x − 3 −5 −1 + (−3) −5 −4 −5 This sentence is true.

Solve these inequalities and graph the solution. Try These: Solve these inequalities and graph the solution. x + 1 −2 −1 −1 Graph: x −3 -5 -4 -3 -2 1 0 1 2 3 x – 7 > – 5 Graph: + 7 + 7 -2 -1 0 1 2 3 4 5 6 7 x > 2

Solve these inequalities and graph the solution. 3 x ≥ 9 Graph: 3 3 x ≥ 3 -2 -1 0 1 2 3 4 5 6 7 < 3 Graph: ( 2 ) . < 3 . ( 2 ) -2 -1 0 1 2 3 4 5 6 7 8 x < 6

Solve this inequality and graph the solution. + 9 +9 4 n > 16 4 4 n > 4 Graph: -2 -1 0 1 2 3 4 5 6 7 8

Solve this inequality and graph the solution. 2x − 8 > −10 + 8 + 8 2x > −2 2 2 x > −1 Graph: -2 -1 0 1 2 3 4 5 6 7 8

Write an inequality for each sentence. In Florida you can vote if you are at least 18 years old. Write an inequality showing the age of all voters in Florida. ( Let x = the voter’s age) x 18 You must be less than 16 years old to play on a certain youth baseball team. Write an inequality showing the age of the players. ( Let n = the player’ s age) n < 16

Write an inequality for each sentence and solve it. Four times a number is less than 12. 4 n < 12 Graph: 4 4 n < 3 -2 -1 0 1 2 3 4 5 6 7 8 The sum of a number and 2 is at least 4. n + 2 4 Graph: −2 −2 n 2 -2 -1 0 1 2 3 4 5 6 7 8

Use an inequality to solve problems. A pair of jeans costs $25 and a shirt costs $10. You have $50 to spend. Write an inequality to find how many shirts you can buy along with one pair of jeans. ( Let n = the number of shirts) 10n + 25 ≤ 50 −25 −25 10n ≤ 25 10 10 n ≤ 2.5 You can buy 2 shirts.