How do you write an inequality and solve given "three fourths of a number decreased by nine is at least forty two"?
The inequality is:
The solution is:
First, let's call "a number" -
"three fourths of a number" then can be written as:
This, "decreased by nine" then can be written as:
"is at least" is the same as
and what it is "at least" is "forty two" so:
To solve this we first add
Now, we multiply each side of the inequality by
Without any punctuation there are different interpretations which lead to different solutions:
Let's use some punctuation so show exactly what is meant:
note how the placement of a comma gives a different meaning.
Let the number be
However, if we interpret it differently we could have: