Solving Inequalities Using Multiplication and Division Algebra 1: Section 3-3 Solving Inequalities Using Multiplication and Division

Objectives: To use multiplication to solve inequalities To use division to solve inequalities

Multiplication Properties: Multiplication, c>0 Multiplication, c<0 For every real number a and b, and for c>0, If a>b, then ac>bc Example: 4> -1, so 4(5) > (-1)(5) If a<b, then ac<bc Example: -6<3, so (-6)(5) < (3)(5) For every real number a and b, and for c<0, If a>b, then ac<bc Example: 4> -1, so 4(-2) < (-1)(-2) If a<b, then ac>bc Example: -6<3, so (-6)(-2) > (3)(-2)

Division Properties Division, c > 0 Division, c < 0 For every real number a and b, and for c>0 If a>b, then a/c>b/c Example: 6>4, so 6/2>4/2 If a<b, then a/c<b/c Example: 2<8, so 2/2<8/2 For every real number a and b, and for c<0 If a>b, then a/c<b/c Example: 6>4, so 6/-2<4/-2 If a<b, then a/c>b/c Example: 2<8, so 2/-2>8/-2

Using the Multiplication Property Multiply by a positive Solve: d > 5 3 6 Multiply by a negative Solve: - t < 1 2

Using the Division Property Solve: -3w > 12 Solve: 5n < -25

Assignment Pg. 149: multiples of 3 (#3-54, 60-72), 82, 83