Inequations

Inequalities are which indicate when a variable is:

• greater than another
• greater than or equal to another
• less than another
• less than or equal to another

Symbols and their meaning

SymbolMeaning
<is less than, so 2 < 5 is a true statement
>is more than, so 6 > 4 is a true statement
$\le$is less than or equal to, so 2 $\le$ 5 is true and so is 2 $\le$ 2.
$\ge$is more than or equal to, so 6 $\ge$ 4 is true and so is 6 $\ge$ 6.

Solving inequalities

An expression such as $$3x - 7 \textless 8$$ is similar to the equation $$3x - 7 = 8$$. However, this time we are looking for numbers which if you multiply by 3, then subtract 7, you get an answer of less than 8.

Unlike $$3x - 7 = 8$$, which has just one answer, there are lots of numbers for which this is true (in fact, an infinite number). So our answer is not a number, but a range of numbers.

Solve inequations just like equations: what you do to one side, you must do to the other.

Example

Solve the equation $$2x + 5\textless17$$

$2x + 5 \textless17$

$2 x \textless17 - 5$

$2x \textless12$

$x \textless12\div2$

$x \textless6$

Question

Solve the inequation $$3x + 2 \textgreater 14$$

$3x + 2 \textgreater 14$

$3x \textgreater 14 - 2$

$3x \textgreater 12$

$x \textgreater 12 \div 3$

$x \textgreater 4$