Writing, Graphing, and Solving Inequalities Writing, Graphing, and Solving

What is an inequality? An inequality compares two values that are not equal. Inequalities have MORE THAN ONE solution.

Symbols < less than > greater than < less than or equal to > greater than or equal to

Inequality Statements “at least” “no more than” “at most” “minimum of” “maximum of” “no less than” ”greatest” “ up to”

Marker Board Practice x is greater than 5 -77 is greater than x -11 is greater than or equal to x x is less than or equal to 58 x is less than or equal to -47

x is equal to 65 -77 is less than x x is greater than to equal to -7 x is greater than -8 x is less than -93

Swim practice will be no more than 35 laps. The mountain is at least 985 feet tall. The movie will be no more than 90 minutes in length. Kevin ran for less than 5 miles.

The occupancy of the room must be less than 437 people. You can not spend more than 50 dollars. More than 800 fans attended the opening soccer game. The heavyweight division is greater than 200 pounds.

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2. Her earnings were no more than $86. 1. More than 40,000 fans attended the opening football game at the University of Florida.   2. Her earnings were no more than $86. 3. A savings account balance is no less than $550. 4. The number of club members is at least 25. 5. The spring calf class at the cattle show is for calves that weigh 825 pounds or less. 6. The minimum deposit for a new checking account is $75.

7. a < 8 8. d ≤ 4 9. b ≥ 11    

Watch this short video on writing inequalities from a number line. https://learnzillion.com/lesson_plans/5388-write-inequalities-given-a-number-line-representation

Write the inequality for each graph.

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1. More than 2,500 people attended the convention. 2. Her earnings were no more than $64. 3. The winning 5K race time was less than 22 minutes. 4. A checking-account balance is no more than $500. 5. A maximum ceiling height of 8 feet was required in the new buildings. 6. A minimum number of 12 participants is required to hold a bike rally.

ROLLER COASTER In order to ride a roller coaster at the theme park, riders must be at least 52 inches tall. Write and graph an inequality to show the safe heights for riders.

FARMING One forklift can raise a maximum of 2,000 kilograms FARMING One forklift can raise a maximum of 2,000 kilograms. Write and graph an inequality to describe the number of kilograms the forklift can raise.

INTERSTATES On interstate highways, the minimum allowable lane width is 12 feet. Write and graph an inequality to show the possible width of a lane.

Finding Possible Solutions for Inequalities Since an inequality uses greater than or less than symbols, one variable inequalities have infinitely many solutions. For example, any rational number greater than 4 will make the inequality x˃4 true.

List 3 possible solutions for each inequality. k ˂ -7 z ≤ 14 m ≤ 2 3/5 f ˃ 0.24 n ≥ 23 p ˃ 16

Of the numbers 5, 6, or 7, which is a solution of the inequality f + 4 < 10? To find which numbers are a solution, replace the variable with each of the numbers. 5 +4 ˂ 10 6 +4 ˂ 10 7 +4 ˂ 10 Which numbers are a solution?

Determine which number is a solution of the inequality.   Is the given value a solution of the inequality? 4. y – 3 < 5, y = 9 5. 14 + s ≥ 22, s = 8 6. r – 5 > 6, y = 10

Determine which number is a solution of the inequality. 2.) 24 – x ≤ 19; 3, 4, 5 3.) 7 + r ≥ 18; 11, 10, 9 4.) 9 – h > 2; 6, 7, 8   ) 32 – n ≤ 17; 13, 14, 15 ) 16 + j ≥ 29; 13, 12, 11 7.) 10 – f < 7; 2, 3, 4 8.) 52 + q < 56; 5, 4, 3

Is the given value a solution of the inequality? 9. 2 + s ≥ 10; s = 7 10. 14 – r < 9; r = 6 11. j – 11 ≥ 20; j = 32 12. t + 6 > 40; t = 35 13. 16 + m > 40; m = 16 14. 9x ≥ 80; x = 9 15. 15 ≤ 3z; z = 4 16. 2n > 26; n = 5