by Shelley Walsh ©2000
Many algebra textbooks, including ours have problems where you are supposed to translate sentences similar to the following one into equations.
Three less than the product of four and a number is the product of four and the sum of the number and seven.
Here is a method that I find helps students keep from getting tied in knots with this.
Find the word 'is' in the sentence and change it into '='.
Three less than the product of four and number = the product of four and the sum of the number and seven.
The equals will divide the sentence into two verbal expressions than can be translated into variable expressions by the methods of my article Translating Verbal Expressions to Variable Expressions.
In this case for the first expression it would go like this.
three less than the product of four and a number
The first thing that would make sense alone here is 'the product of four and a number', so put parentheses around it.
three less than (the product of four and a number)
'the product of four and a number' can be translated to 4x, so this is
three less than (4x).
If I want to compute the number than is three less than a number, then I subtract 3 from the number, so this becomes
4x-3
I can drop the parentheses around the 4x here, because multiplication comes before subtraction in the order of operations agreement.
For the second expression we have
the product of four and the sum of the number and seven
'the sum of the number and seven' is an expression that can stand alone, so put parentheses around it.
the product of four and (the sum of the number and seven)
It can be translated to x+7, so this becomes
the product of four and (x+7)
This then becomes
4(x+7).
Then putting the whole sentence together, it says
4x-3=4(x+7).
See Linear Equations to find out how to solve it.