Page 472 - Algebra 1

When dividing an inequality by a positive value, the order of the inequality
does not change.
__ __ 6 > 4, so 6 > 4 . 8 < 12, so 8 < 12 .
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Division Property of Inequality for c > 0
For every real number a and b, and c > 0:
If a>b,then_a >_b. If a<b,then_a <_b.
This property is also true for ≥ and ≤.
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Example
3
Dividing by a Positive Number
Solve, graph, and check the solution for the inequality 18 > 3r. SOLUTION
Solve the inequality.
18 > 3r
__
18 > 3r Division Property of Inequality for c > 0
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6 > r Simplify.
Caution
When the variable is on the right side of the inequality, be careful to read the inequality symbol correctly. 6 > r means that r is less than 6.
Graph the solution on a number line.
Check
Check the endpoint.
18 3r
18 3(6) 18=18 ✓
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Check the direction of the inequality.
18 3r
18 3(5) 18>15 ✓
Both statements are true so the solution is correct.
When dividing an inequality by a negative value, the order of the inequality
changes.
6 > 4, so _6 < _4 . 8 < 12, so _8 > _12 . -2 -2 -4 -4
Division Property of Inequality for c < 0
For every real number a and b, and c < 0:
If a>b,then_a <_b. If a<b,then_a >_b.
This property is also true for ≥ and ≤.
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Lesson 70 457