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Solving Inequalities Algebraically

Anything involving any of the expressions:

< less than

> greater than

≤ less than or equal to

≥ greater than or equal to

is an inequality. There are fundamentally two sorts of inequalities:

One sided, or simple inequalities such as 4x-1<3

Two sided inequalities such as

Solving inequalities is a bit like solving equations. For the example above:

Add 1 to both sides

Divide by 4

For the second example:

Add one 1 to ALL sides as shown

To give

Now divide by 4.

In this example, ifwhere a whole number, it could be any of 2, 3, 4, 5, 6, 7. Notice because of the < sign,cannot be equal to 1.

Example: Find the largest integerthat satisfies

Add 1 to both sides

Divide by 4

Sinceis an integer, the largest integer less that 4.5, it must be 4.

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