Ch. 1-4 Solving Inequalities

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

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

Ex. 1: Solve -2x < 3(x – 5). Graph the solution

• -2x < 3(x - 5)

-2x < 3x - 15

-3x -3x

-5x < -15

X > 3

Ex. 2: Solve 7x > 7(2 + x). Graph the solution.

7x > 7(2 + x)

7x > 14 + 7x

-7x -7x

0> 14; no solution

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

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

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

Homework

• P. 29 # 1 – 13 odd, 22 – 24, 39 – 49 odd