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
