6.2 Solving inequalities by multiplication If any positive number is multiplied to each side of a true inequality, the resulting inequality is also true. For example: 3 < 8 3(2) < 8(2) 6 < 16 Example 1:

Multiplication by a negative number If any negative number is multiplied to each side of a true inequality, the direction of the inequality symbol must be reversed so that the resulting inequality is also true. For example: 3 < 8 3(-2) < 8(-2) -6 > -16 Example 2:

Write an inequality for the sentence below. Four-fifths of a number is at most twenty. 4/5x 4/5x 4/5x 20 Solve 4/5x 20 (5/4) 4/5x 20 (5/4) x  100/4 x  25 {x | x < 25}

Division by a positive number If each side of a true inequality is divided by the same positive number, the resulting inequality is also true. For example: 2 < 8 2/2 < 8/2 1 < 4 Example 4:

Division by a negative number If each side of a true inequality is divided by any negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true. For example: 2 < 8 2/-2 < 8/-2 -1 > -4 Example 5:

Try These p. 305 2-12 even Assignment #40 p. 305 13-41 odd, 54, 56, 57