Math 7 ( Period 4)

Solving Inequalities Using Multiplication or Division 9.7

Solving an inequality is similar to solving an equation. You can use the four arithmetic operations to isolate the variable on one side of the inequality There is ONE important difference.

DAY TWO of this lesson (January 6)  

When you multiply an inequality by a negative number, you must reverse (switch) the inequality symbol!

5 > -4 but if you multiply both sides by -2

-10 < 8

Divide  by -3:    -6 < 3 becomes 2 > -1

Properties of Inequalities

1. Adding or subtracting the same number on each side of the inequality produces an equivalent inequality.

2. Multiplying or dividing each of an inequality by the same positive number produces an equivalent inequality.

3. Multiplying or dividing each of an inequality by the same negative number AND reversing the direction of the inequality symbol produces an equivalent inequality.

-2x < 6

Divide each side by -2 and as you do that rewrite the inequality reversing the inequality symbol

-2x/-2 > 6/-2

x > -3

-1/2(x) ≥ 6

This time you need to multiply by -2 and as you do that rewrite the inequality reversing the symbol

(-2)(-1/2)x ≤ 6(-2)

x ≤ -12

What about 6x > -42

You are not multiplying or dividing by a negative number—so just divide both sides

6x/6 > -42/6

x> -7