Inequations
Watch this video to learn about working with inequations.
Inequalities are expressionNumbers, symbols and operators grouped together - one half of an equation, eg 2bf + 2f + 3k. 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
| Symbol | Meaning |
| < | 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. |
| Symbol | < |
|---|---|
| Meaning | is less than, so 2 < 5 is a true statement |
| Symbol | > |
|---|---|
| Meaning | is more than, so 6 > 4 is a true statement |
| Symbol | \(\le\) |
|---|---|
| Meaning | is less than or equal to, so 2 \(\le\) 5 is true and so is 2 \(\le\) 2. |
| Symbol | \(\ge\) |
|---|---|
| Meaning | 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 \(3x + 2 \textgreater 14\)
\(3x + 2 \textgreater 14\)
\(3x \textgreater 14 - 2\)
\(3x \textgreater 12\)
\(x \textgreater 12 \div 3\)
\(x \textgreater 4\)
