Inequalities

An inequality is a statement that one amount or quantity is greater than (or equal to) or less than (or equal to) another amount or quantity.  The following symbols are used to represent inequalities:

< means Less than

Example: 10 < 5

< means Less than or equal to

Example: 7 < 4 + 3

> means Greater than

Example: 20 > 15

> means Greater than or equal to

Example: 8-5 > 3

Inequalities can also be solved as equations.

Here’s an example of an equation where we want to solve for x:

5x – 10 = 20

We would add 10 to each side to get:

5x = 30

Then, we would divide each side by 5, so x = 6.

Similarly, we can use the same method if this were an inequality:

5x – 10 > 20

We would add 10 to both sides to get:

5x > 30

Then, we would divide each side by 5, so x > 6.

An important concept to keep in mind is that when you divide or multiply each side of an inequality by a negative amount, you must reverse the Greater than (or equal to) sign or the Less than (or equal to) sign.

Here’s an example:

-3x - 6 < 9

We would add 6 to each side to get:

-3x < 15

Then, we would divide each side by -3 to get:

x < -5

However, because we divided by a negative amount, we must reverse the sign to get the final answer of:

x > -5