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.
