# Solving Inequalities Warm Up Solve the following equations

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Solving Inequalities

Warm – Up!! Solve the following equations 1. 7 = x – 8 2. 2 m + 3 = 31 3. 3 x – 12 = 27

One Step Inequalities An inequality says that two values are not equal and we can represent/ show they are not equal in 4 different ways. <: >: Inequalities are similar to equations!

Solving One-Step Inequalities Treat the inequality symbol (<, >, ≤, ≥) as an equal sign and solve. If you multiply or divide by a negative number the inequality symbol flips the opposite way. Examples: 1. ) x – 7 > 10 2. ) 2 d < 21

Is It A Solution? You can determine if a given value is a solution to the inequality by evaluating an expression. Example: Are the following values solutions of x < 9 A. ) 6 B. ) -2 C. ) 18 2

Solving Multi Step Inequalities When solving multi-step inequalities, treat the inequalities (<, >, <, >) like equal signs Remember to flip the inequality when multiplying or dividing by negative numbers Example: Simplify and graph the inequality -2(m – 3) > 14

Practice 1. ) Is 3 a solution to 2 - 4 x > 14? 2. ) Is -2 a solution to 10 > 9 x - 4? 3. ) 2 k +4 < k + 8 4. ) 2 j – 10 – 9 j > -3

More Practice 5. ) b > 9 6. ) j < 10 + 7 -2 7. ) -7 x > 14 8. ) 6 + d > 3

Exit Ticket Solve the following inequalities: 1) y + 5 > 9 2) -8 x < 64 3) Simplify the following inequality and graph it on a number line: 10 w – 7 w + 8 > 20

Warm – Up!! Solve the following inequalities: 1) 2 - m > 12 2) -8 k < 64 Solve the following equations for c: 1) 10 c – 3 = 13 c 2) c + 1 = 4 2

Translating Write and solve the following equations: 7=x– 8 2 m + 3 = 31 Write an equation modeling the following: The sum of 9 and k is 18 Seven minus v is 3 23 less than x is 10

From English To Inequality Look for the key terms: less, more/greater, less than or equal to, greater/more than or equal to, at least, at most Examples: Translate the following 1. ) You have to be at least 48 inches to ride the rollercoaster. ________ 2. The speed limit is 65 miles per hour. _______

Practice A number plus seven is less than 12. _____________ 5 less than a number is 2. _____ The standard size, s, of adult shoes ranges from size 3 to size 25. Employees must work at least 20 years in order to receive full benefits. __________

Practice Mrs. Smith wrote “Eight less than three times a number is greater than 15” on the board. If x represents the number, which inequality is a correct translation of this statement? (A) (B) (C) (D) 3 x – 8 > 15 3 x – 8 < 15 8 – 3 x > 15 8 – 3 x < 15

Practice Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm, Which inequality represents the range of heights? (A) (B) (C) (D) 155 < h < 190 154 < h < 190

Practice