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# How do I solve linear inequalities?

By David Moody on the 11th of June, 2012

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First, treat the inequality like a standard linear equation (e.g. X+3=0).  Move all the unknown variables to one side of the equation and the rest of the numbers to the other side.  Reduce the expression with the unknowns.

By brian on the 16th of January, 2013

## Solve linear inequalities

An inequality says that whatever’s on one side is either bigger, or smaller, than what’s on the other side (depending on the sign).

e.g. x + 3 < 6

We can solve this inequality similarly to sign simply being an equals sign, but instead of one answer, we now have a set of values that could work as the answer.

The process for this is identical to the process for solving regular equations, with only one exception:

Whenever you multiply or divide by a negative number, you flip the inequality sign

Example 1

– 2x > 6

In the next step, I’m going to divide all the terms by -2, and so must flip the inequality sign

x < -3

## Follow the links below to see how this topic has appeared in past exam papers

Excel November 2010 (H) - Page 9, Question 10

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