Inequalities are expressions which indicate when a variable is:
|<||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.|
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.
Solve the equation \(2x + 5\textless17\)
\[2x + 5 \textless17\]
\[2 x \textless17 - 5\]
\[x \textless12\div2 \]
Solve the inequation \(3x + 2 \textgreater 14\)
\[3x + 2 \textgreater 14\]
\[3x \textgreater 14 - 2\]
\[3x \textgreater 12\]
\[x \textgreater 12 \div 3\]
\[x \textgreater 4\]