Inequalities

Writing Inequalities

< ≤ > ≥ SYMBOL MEANING KEY WORDS TO HELP DECIDE WHAT SYMBOL TO USE < Is less than Fewer than, below ≤ Is less than or equal to At most, no more than, maximum > Is greater than More than, above ≥ Is greater than or equal to At least, no less than, minimum

WRITE AN INEQUALITY TO REPRESENT THE SITUATION 1. You must be at least 42 inches tall to ride the bumper cars. x ≥42 2. Children under 36 inches in height cannot ride the roller coaster. x<36 3. To ride an amusement park ride, you must be 48 inches tall or taller. x≥48 4. A restaurant can hold at most 40 people. x≤40 5. Adults 65 and over will get a discount at the restaurant. x≥65

x≥62 x<12 𝑥≥10 𝑥≥35 WRITE AN INEQUALITY TO REPRESENT THE SITUATION 6. People aged 62 or older receive a discount on their meals. x≥62 7. Children under 12 will be admitted to the museum at no charge. x<12 8.In football, you need to gain at least 10 yards for a first down. 𝑥≥10 9. To run for president of the United States, you must be at least 35 years old. 𝑥≥35

Solving Inequalities

Solving Inequalities Combine like terms Isolate the variable using inverse operations (solve like equations) Decide if Closed or Open Circle Graph the Inequality

Example 1: Solving and Graphing Inequalities Solve and graph the inequality. x + 2  8 –2 –2 Subtract 2 from both sides. x  6 1 2 3 4 5 6 7

Solve and graph the inequality. +4 +4 Add 4 to both sides. g < 14 9 10 11 12 13 14 15

Solve and graph the inequality. 9 9 Divide both sides by 9. p ≥ 11 9 10 11 12 13 14 15

Solve and graph. × 4 1 4 1 × a 4 > 12 Multiply both sides by 4. > 12 Multiply both sides by 4. a > 48 43 44 45 46 47 48 49 50 51 52 53 54