Symbols, solving inequalities and graphs
An inequality such as 3x - 7 < 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.
We solve these inequalities just like simple equations: what you do to one side, you must do to the other.
Now have a look at this typical question:
Solve the expression 3x - 7 < 8.
So the inequality in 3x - 7 < 8 is satisfied when x is less than 5. (Note that this does not include 5 itself.)
Sometimes the unknown appears on both sides, just as in simple equations.
Now look at this question.
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