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Solving first degree inequations in one unknown

A first degree inequation, in one unknown, is an inequality relation in the following form:

ax + b 0 or ax + b > 0
ax + b 0 or ax + b < 0

To solve a first degree inequation, in one unknown, simply isolate the unknown.

We thus obtain the solution set, that is, the set of values which satisfies the inequation.

Operations on inequations

Law 1

We may add or subtract a similar quantity from each of the members of an inequation and obtain an equivalent inequation , i.e., an inequation with the same solution set.

For example, if 5x + 3 2x - 4
then 5x + 3 - 3 2x - 4 - 3
and 5x 2x - 7

Law 2

We may multiply or divide each of the members of an inequation by a positive quantity and obtain an equivalent inequation.

For example, if 4x 8
then X 4x X 8
and x 2

Law 3

We may multiply or divide each of the members of an inequation by a negative quantity and obtain an equivalent inequation; however, you must reverse the inequality.

For example, if -4x 8
then - X (-4x) - X 8
and x -2

Example 1

Solve the following inequation; 10x - 8 > 6x + 4

10x - 6x - 8 + 8 > 6x - 6x + 4 + 8

4x > 12

X 4x > X 12

x > 3

Example 2

Solve: 5x - 3 8x - 12

5x - 8x - 3 + 3 8x - 8x - 12 + 3

-3x -9

- X (-3x) - X (-9)

x 3

Before proceeding to the questions, ensure that you have some paper and a pencil handy.


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