Dictionary for Basic and Intermediate Algebra
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INEQUALITIES

To solve linear inequalities follow the same procedure used for linear equations, but remember that the direction of the inequality should be reversed if you multiply or divide both sides of an inequality by a negative number. We now list three inequality properties below:

Example 1) Solvethe inequality 7x - 3  >  5x + 9

Solution:

Grouping the x on the left side 7x - 5x > 9 + 3

Collecting like terms   2x > 12

Dividing by 2 x > 6

Answer: x > 6

 

Example 2) Solve the inequality3(2x - 5) + 4 < 2(5x + 3) + 3

Removing parenthesis 6x - 15 + 4 < 10x + 6 + 3

Collecting like terms6x -11 < 10x + 9

Grouping the x on left side 6x -10x < 9 +11

Collecting like terms  - 4x < 20

Dividing by - 4 (Change orientation) -4x / -4 > 20 / -4

Answer x > - 5

 

Example 3) Solve  wpe4.jpg (1667 bytes)  , use interval notation to write your answer.

Multiplying the inequality by the LCM (=20) we get

wpe5.jpg (8139 bytes)
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