Solve Inequalities Using Division

When you solve an inequality containing the operation multiplication you need to use the division property of inequality.

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The Division Property of Inequality:

When you divide both a and b by a positive number, the inequality stays the same.

But when you divide both a and b by a negative number, the inequality swaps over!

Here are the rules:

• If a < b, and c is positive, then a/c < b/c
• If a < b, and c is negative, then a/c > b/c (inequality swaps over!)

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From: http://www.mathsisfun.com/algebra/inequality-properties.html

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Again you must remember that when you divide both sides by a positive number the inequality stays the same, however when you divide both sides by a negative number you need to switch the inequality.

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Example: Solve for y:

3y ≥ 15

3 3 Use the division property of inequality

y ≥ 5

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The solution set is all real numbers greater than or equal to 5.

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Example: Solve 6 ≥ -2b

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6 ≥ -2b b is multiplied by a -2

-2 -2 Use the division property of inequality

-3 ≤ b you divided both sides by a negative number you need to flip the

inequality

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The solution set is all real numbers greater than or equal to -3.

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Let’s try some:

7n > -21 -12w < 96

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