Algebra 1
Section 4.2
Properties of Inequality
As with equations, adding or
subtracting the same number
on both sides of an inequality
produces an equivalent
inequality, having the same
solutions as the original
inequality.
Addition Property of Inequality
If a, Addition
The
b, and c are
Property
real numbers
of
Inequality
or
expressions
holdssuch
for any
thatofathe
< b,
five inequality
then
a + c < b symbols.
+ c.
Example 1
x+7<8
x+7–7<8–7
x<1
Example 1
x–5≠3
x–5+5≠3+5
x≠8
Example 1
-0.6 ≤ x – 0.4
-0.6 + 0.4 ≤ x – 0.4 + 0.4
-0.2 ≤ x
x ≥ -0.2
Properties of Inequality
What happens if you multiply
both sides of an inequality by a
positive number?
What happens if you multiply
both sides of an inequality by a
negative number?
Multiplication Property of Inequality
If a, b,
The
Multiplication
and c are real
Property
numbers
of
Inequality
or
expressions
has similar
such that
results
a < b,
for
>, ≤, or ≥. Remember to
and...
reverse
inequality
1) c > 0,the
then
ac < bc. symbol
when multiplying or dividing
2) c < 0, then ac > bc.
both sides of the inequality by a
negative number.
Example 2
-3x < -9
-3x <
-9
>
-3
-3
x>3
Example 2
x
> -4
12
x
12
> 12(-4)
12
( )
x > -48
Example 2
5
x ≥ 25
2
2
5
2
x ≥
≤ (25)
5
2
5
( )
x ≤ -10
Example 3
P
r
t
=
I
P 0.07 1 = 0.07P
0.07P ≥ 875
7P ≥ 87,500
P ≥ 12,500
$12,500 or more must be invested.
Homework:
pp. 151-152