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# Linear equations

### What are inequalities?

• We are familiar with the use of the symbol $$=$$ to mean what is on the left hand side equals that on the right hand side.
• If this is not so, that is, the left hand side does not equal the right hand side, then we use the symbol $$\ne$$, meaning ‘not equal to’. For  example, we can say that $$7 \ne 3$$ (read as $$7$$ is not equal to $$3$$).
• We can also use other symbols:
 $$<$$ Less than $$\leq$$ Less than or equal to $$>$$ Greater than $$\geq$$ Greater than or equal to
• We can graph inequations to help visualise their properties and solution.
• The inequality $$x > 2$$ is read as ‘$$x$$ is greater than two’. We can represent this inequation on a real number line.

• Another example is: $$1 < x \leq 3$$, read as '$$x$$ is greater than one but less than or equal to three'. We can represent this inequality on a real number line as: