Solving-Linear-Inequalities Wjec-Eduqas Foundation

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Exam code:C300

Solving linear lnequalities

How do I solve a linear inequality?

Solving linear inequalities is just like Solving Linear Equations
- Follow the same rules, but keep the inequality sign throughout
- If you change the inequality sign to an equals sign you are changing the meaning of the problem
When you multiply or divide both sides by a negative number, you must flip the sign of the inequality
- E.g.
  $space 1 less than 2 open parentheses cross times negative 1 close parentheses space space space space space space space space space space space space space space space space space space space open parentheses cross times negative 1 close parentheses space minus 1 greater than negative 2$
Never multiply or divide by a variable (x) as this could be positive or negative
The safest way to rearrange is simply to add and subtract to move all the terms onto one side

How do I solve double inequalities?

Inequalities such as $a space less than space 2 x space less than space b$ can be solved by doing the same thing to all three parts of the inequality
- Use the same rules as solving linear inequalities

Examiner Tips and Tricks

Do not change the inequality sign to an equals when solving linear inequalities.
- In an exam you will lose marks for doing this.
Remember to reverse the direction of the inequality sign when multiplying or dividing by a negative number!

Worked Example

Solve the inequality $2 x minus 5 less or equal than 21$ .

Add 5 from both sides

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