Inequalities Objectives: 1. To identify symbols that represent inequalities 2. Write inequalities to represent situations 3. Graph inequalities on a number line 4. Use addition and subtraction to solve inequalities

≤ Terminology: Inequality: A mathematical sentence that contains _____, _____, _____, or _____ used to compare the values of two expressions. Inequality symbols: ≤ > < > - is less than - is fewer than - is greater than - is more than - exceeds - is less than or equal to - is no more than - is at most Important! The open side represents the __________ value The closed side represents the _________ value. Example: 4 12 0 -5 When graphing inequalities, you use a ________________.

Write an inequality to represent each sentence: 1. Your age is greater than 14. a. define your variable: Let a = ______________ b. write your inequality: _____________________ 2. The restaurant can seat at most 172 people. Let p = ___________________ ___________________________

Translating verbal statements into mathematical/algebraic inequalities: 1. Two less than a number 2 < x 2. Four more than a number is greater than or equal to five x + 4 > 5 3. The maximum value of a number is 28 x < 28 4. The sum of a number and nine is at least 81 x + 9 > 81 5. X is greater than or equal to 1 x > 1

Translating Practice: 1. The restaurant can seat no more than 164 people. - select and define your variable - write your inequality 2. At least 425 students can attend the concert.

Graph an inequality: Steps: 1. Draw and label a ________________________ 2. Place a closed circle ( for ____ or ____) or an open circle (for ____ or ____) on the value in the expression. 3. Draw a line with an ________, in the direction that represents the ____________ to the inequality. Examples: 1. x < 8 2. x > -4

Practice:

Writing an inequality to represent a graph: 1. Determine what _______________________ to use based on the open or closed circle 2. Find the ____________ of the number the graph represents 3. Pick a ______________ 4. Write your inequality

Write an expression that matches the graph of each inequality: 1. 2. 3.

Solving inequalities using Addition/Subtraction: Key: solving inequalties using addition and subtraction is just like equation solving with addition and subtraction. Examples: 1. 10 > x + 4 2. x - 15 < -6 3. d + 6 > 23 4. a + 3.3 < 2.6

Practice: 1. v - 4 > 12 2. 6 > c + 31 3. -3 > f - 12 4. 5 < -52 + m

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