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EXAMPLES & SOLUTIONS
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Inequalities are mathematical expressions, in which one side is not equal to the other.
Inequalities are similar to solving equations, except there isn't an equal sign.
Because of this, it can have more than one solution.
It utilizes the operators, <, >, < , and >
When multiplying or dividing by a neg. number, the result switches the direction of the original operator.
INEQUALITY PROPERTY
Visual explanation of the meaning of the direction of inequalities
Formula:
Pos
a > 0
-a < 0
Neg
a > 0
-a > 0
means greater than OR less than
means greater than and equal OR less than and equal
arrow display numbers that continue to infinity
x > 3
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x > 3
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x < -3
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x < -3
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Inequality Examples
Rules with examples
Formula:
if a > b, then
a + c > b + c
Addition
if a = 20, b = 5, c = 4 ​if 20 > 5,
then,
20 + 5 > 5 + 4
25 > 9
Formula:
if a > b, then
a - c > b - c
Subtraction
if a = 20 b = 5, c = 4​if 20 > 5,
then,
20 - 4 > 5 - 4
16 > 1
Formula:
if a < b, then
a + c < b + c
Addition
if a = 5, b = 25, c = 4 ​if 5 < 25,
then,
5 + 5 < 25 + 4
10 < 29
Formula:
if a < b, then
a - c < b - c
Subtraction
if a = 5, b = 20, c = 5 ​if 5 < 20,
then,
5 - 5 < 20 - 5
0 < 15
Formula:
if c > 0, then
if a > b, then ac > bc
if a < b, then ac < bc
Multiply
if a = 20, b = 5, c = 4
when a > b, then,
20 * 4 > 5 * 4
80 > 20
if a = 5, b = 20, c = 4
when a < b, then,
5 * 4 < 20 * 4
20 < 80
Formula:
if c > 0, then
if a > b, then
a b
>
c c
if a < b, then
c c
a b
<
Divide
if a = 20, b = 5, c = 5
when a > b, then,
20 > 5
1 > 4
if a = 5, b = 20, c = 5 when a < b, then,
5 < 20
1 < 4
5 5
5 5
REVERSE SIGNS
Rules to follow when multiplying or dividing by a neg. number
Formula:
if c < 0, then
if a > b, then ac < bc
if a < b, then ac > bc
Multiply
if a = 20, b = 5, c = -5
when a > b, then,
20 * -5 < 5 * -5
-100 < -25
if a = 5, b = 20, c = -5
when a < b, then,
5 * -5 > 20 * -5
-25 > -100
Formula:
if c > 0, then
if a > b, then
a b
<
c c
if a < b, then
c c
a b
>
Divide
if a = 20, b = 10, c = -5
when a > b, then,
20 < 10
-4 < -2
-5 -5
if a = 10, b = 20, c = -5
when a < b, then,
10 > 20
-2 > -4
-5 -5
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