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1-4 Solving Inequalities

1-4 Solving Inequalities. Big Idea: -Solve equations and inequalities. Solving and Graphing Inequalities. As with an equation, the solutions of an inequality are the numbers that make it true. The properties for solving inequalities are similar to the properties for solving equations.

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1-4 Solving Inequalities

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  1. 1-4 Solving Inequalities Big Idea: -Solve equations and inequalities.

  2. Solving and Graphing Inequalities As with an equation, the solutions of an inequality are the numbers that make it true. The properties for solving inequalities are similar to the properties for solving equations. The exception occurs when you multiply or divide each side by a negative. MULTIPLYING OR DIVIDING BOTH SIDES BY A NEGATIVE REVERSES THE INEQUALITY SYMBOL!

  3. Dividing 3x ≥ 15 Multiplying

  4. Ex 1: solve and Graph each solution. A) -2x < 3(x – 5)

  5. B) 7x > 7(2 + x)

  6. Compound Inequalities Compound Inequality: a pair of inequalities joined by “and” or “or”. Ex: -1 < x and x ≤ 3 same as -1 <x ≤ 3 x < 2 or x ≥ 5

  7. To solve a compound inequality containing “and”, find all values of the variable that make both inequalities true. -Name a student that is a girl and wearing red -Name a teacher that is female and is short -Find x such that x > 2 and x ≤ 5.

  8. To solve a compound inequality containing “or”, find all values of the variable that make at least one of the inequalities true. -Name a sport that involves water or a puck. -Name a teacher that is male or teaches Lang. Arts. -Find x such that x < 0 or x ≥ 5.

  9. Ex 2: Graph the solution. A) 2x – 1 < 3x and x > 4x – 9.

  10. B) 3x + 9 < -3 or -2x + 1 < 5.

  11. Classwork/Homework: • Page 24 #3-11, 17-28

  12. Essential Question: What are the similarities and differences between inequalities and equations? Answer on your paper in complete sentences.

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