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Solving Inequalities: Part 2 Chapter 4.6 Multiplying and Dividing in Inequalities: If you multiply or divide both sides by a negative number, then you must reverse the inequality sign. Solve: –4x < 12 Divide by NEGATIVE 4 4 x 12 4 4 x > -3 Change the “less than” sign to “greater than.” Why reverse the inequality sign? –4x < 12 x < -3 Suppose we didn’t reverse our sign. x is less than –3. Try examples -4(-5) < 12 20 < 12, 20 is NOT less than 12. -4(-10) < 12 40 < 12 40 is NOT less than 12. Fractions: Solve and graph your solution on a number line: 2 8 y 3 Multiply by the reciprocal. 3 3 2 8 y 2 2 3 12 y Because we are multiplying by a negative, we reverse the sign. Graph the Inequality: 12 y We use a closed circle. Negative 12 is greater than or equal to y. -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 If you don’t know which way the arrow should go, try plugging in a number and seeing if it makes a true statement. Other Examples: Try to solve in notebook. x 100 4 We are dividing x by a negative 4. So, we must multiply both sides by negative 4. x 4 100 4 4 x 400 Don’t forget to switch the inequality sign! Graphing Inequalities: You choose the scale. x 400 If you have very large, or very small numbers, remember that you can choose how you label your number line. -600 -500 -400 -300 -200 -100 x is less than or equal to –400, so x could be –500 or –600. 0 Fractions and Inequalities 5 1 p 6 3 The variable is multiplied by negative 1 . 3 3 5 3 1 So we must multiply both p sides by the reciprocal. 16 1 3 15 p 6 Don’t forget to switch the inequality sign! Graphing Fractions and Mixed Numbers On a number line: Turn any improper fractions into mixed numbers. 1 2 p 2 15 1 2 6 2 -4 -3 -2 -1 0 Homework: Page 188-189 (17-43 odds) SHOW WORK. Solution on numberline!