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
\[\le\]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 \(2x + 5\textless17\)

Answer

\[2x + 5 \textless17\]

\[2 x \textless17 - 5\]

\[2x \textless12\]

\[x \textless12\div2 \]

\[x \textless6\]

Question

Solve the inequation \(3x + 2 \textgreater 14\)

\[3x + 2 \textgreater 14\]

\[3x \textgreater 14 - 2\]

\[3x \textgreater 12\]

\[x \textgreater 12 \div 3\]

\[x \textgreater 4\]