# Inequalities on number line

A statement involving a variable and a sign of inequality (viz. < , ≤ , > or ≥) is called an

**inequality**. A statement of inequality between two expressions consisting of a single variable, say x, of highest power 1, is called a

**linear inequality in one variable**. It is ussually written in any of the following forms:

ax+b<0

ax+b>0

ax+b≥0

ax+b≤0

where a ≠ 0;

Linear inequalities are solved much the same way as linear equations are solved, with one important exception: when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.

<\;3\;\Rightarrow\;2x\;<\;3+5\;\Rightarrow\;2x\;<\;8\;\Rightarrow\;x\;<\;4 align='absmiddle'>

<\;4\;\}\;\text{=}\;\(-\infty,4) align='absmiddle'>

What inequality does this number line show?

Write your answer starting with x (for example, x<3).

Solution:

Remember,

A filled-in circle includes the number it is located on.

An open circle does not include the number it is located on.

We want to write an inequality that says x can be anything shown by the arrow and circle. The open circle located on 6 means that x cannot be equal to 6. The arrow pointing to the right means that x can be any number greater than 6.

Since x can be any number greater than 6, the inequality is x > 6 .