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Ch. 1-4 Solving Inequalities
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Properties of Inequalities
• Transitive Property: – If a < b, and b < c, then a < c
• Addition Property: – If a < b, then a + c < b + c
• Subtraction Property:– If a < b, then a – c < b - c
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Properties of Inequalities (cont.)
• Multiplication Property:
– If a < b and c > 0, then ac < bc.
– If a < b and c < 0, then ac > bc.
• Division Property:
– If a < b and c > 0, then
– If a < b and c < 0, then
a b
c c
a b
c c
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Ex. 1: Solve -2x < 3(x – 5). Graph the solution
• -2x < 3(x - 5)
-2x < 3x - 15
-3x -3x
-5x < -15
X > 3
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Ex. 2: Solve 7x > 7(2 + x). Graph the solution.
7x > 7(2 + x)
7x > 14 + 7x
-7x -7x
0> 14; no solution
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Ex. 3: A real estate agent earns a salary of $2000 per month plus 4% of the sales. Find the sales if the salesperson is to have a monthly income of at
least $5000
• 2000 + (.04)x > 5000
-2000 -2000
.04x > 3000
x > 75,000
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Ex. 4 Graph the solution of 2x – 1< 3x and
x > 4x – 9 2x – 1 < 3x x > 4x - 9
-2x -2x
-1 < x
-4x -4x
-3x > -9
x < 3
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Ex. 5: Graph the solution of 3x + 9 < -3 or -2x + 1 < 5
3x + 9 < -3 -2x + 1 < 5
-9 -9
3x < -12
x < -4
-1 -1
-2x < 4
x > -2
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Homework
• P. 29 # 1 – 13 odd, 22 – 24, 39 – 49 odd