Lesson 2 Solving Inequalities Using Multiplication and Division

Bell Ringer Solve the following equations. 3x = 9 z/4 = 3 4y = 16 (1/2)m = 4 (click for answers) If you got: x = 3 z = 12 y = 4 m = 8 GREAT JOB!

Show me how you got the bell ringer. 3x = 9 (undo the multiplication with division) 3/3 x = 9/3 (simplify both sides) x = 3 You can check your answer by substituting the value of x into the original equation. 3(3) = 9 : this is a true statement, therefore x = 3 is correct! = 3 (undo the division with multiplication) 4( )= 3(4) Z = 12 4y = 16 4/4y = 16/4 (divide both sides by 4) y = 4 4. (1/2)m = 4 (mult. by the inverse of (1/2) (2/1)(1/2)m = 4(2/1) m = 8

Multiplying by a Positive Number If each side of a true inequality is multiplied by the same Positive number, the resulting inequality is also true. Algebraically: If a and b are any numbers and c is a positive number, the following are true. If a > b, then ac > bc, and if a < b, then ac < bc Example: 6 > 5, then 6(3) > 5(3) 18 > 15

Multiplying by a Negative Number If each side of a true inequality is multiplied by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true. Algebraically: If a and b are any numbers and c is a negative number, the following are true. If a > b, then ac < bc, and if a < b, then ac > bc. Example: 5 > 4, then 5(-2) < 4(-2) -10 < -8 √

Dividing by a Positive Number If each side of a true inequality is divided by the same Positive number, the resulting inequality is also true. Algebraically: If a and b are any numbers and c is a positive number, the following are true. If a > b, then a/c > b/c, and if a < b, then a/c < b/c Example: 9 > 6, then 9/(3) > 6/(3) 3 > 2

Dividing by a Negative Number If each side of a true inequality is divided by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true. Algebraically: If a and b are any numbers and c is a negative number, the following are true. If a > b, then a/c < b/c, and if a < b, then a/c > b/c. Example: 6 > 4, then 6/(-2) < 4/(-2) -3 < -2 √

Here’s Some Problems 6g < 144 -14d > 84 -(3/4)q < -33 Five times a number is less than or equal to ten. Hint: 5n < 10 If you got: g < 24 d < -6 q > 44 n < 2