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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Inequalities

Property of Comparisons
For all real numbers a and b, one and only one of the
following statements is true:
a < b, a = b, or a > b

Suppose you know two facts about the graphs of
three numbers a, b, and c.

1) The graph of a is to the left of the graph of b:
a < b

2) The graph of b is to the left of the graph of c:
b < c

From the graph above, you can see that the graph
of a is to the left of the graph of c: a < c

Transitive Property of Order
For all real numbers a, b, and c:

1) If a < b and b < c, then a < c.
2) If c > b and b > a, then c > a.

What happens when the same number is added
or subtracted to each side of an inequality?

3 6
3 6
3 + 4 _____ 6 + 4
3 - 4_____ 6 - 4
7 10
-12

Addition Property of Order
For all real numbers, a, b and c:

1) If a < b, then
2) If a > b, then a + c > b + c

What happens when the same number is
multiplied on each side of an inequality?
4 -3
4 -3
4(2) _____ -3(2)
4(-2)_____ -3(-2)
8 -6
-8 6

Multiplication Property of Order
For all real numbers a, b, and c such that

 c > 0 (c is positive): c < 0 (c is negative) 1) If a < b, then ac < bc 2) If a > b, then ac > bc

What would happen if we multiplied
both sides of an inequality by 0?

Example 1: Solve the inequality.

Example 2: Solve 6x - 3 < 7 + 4x and graph the
solution set.

Example 3: Solve 2(w - 8) + 9 ≥ 3(4 - w)- 4
and graph its solution set.

Example 4: Solve 4x > 4 (x + 2)
and graph its solution set.

Example 5: Solve y + 5 < 7y - 6(y - 1)
and graph its solution set.