Inequations

Inequalities are expressions 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
\leis less than or equal to, so 2 \le 5 is true and so is 2 \le 2.
\geis 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

Answer

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