Translate the following statement into an algebraic
equation. Let x represent the number.
6 times a number is 14 more than that number.
After each step, I'll color some of the words red, then
I'll replace them. Then I'll copy it over with some new
words colored red.
6 times a number is 14 more than that number.
Replace the words "a number" by x. Now we have:
6 times x is 14 more than that number.
6 times x is 14 more than that number.
Replace the word "that number" also by x. Now we have:
6 times x is 14 more than x.
6 times x is 14 more than x.
Replace the words "6 times x" by "6x". Now we have
6x is 14 more than x.
6x is 14 more than x.
Now we need to replace the words "14 more than x"
by something.
This is a little harder but not much. To get 14 more
than x, we start with x, so we write x first, then we
want to make it 14 more by adding ("plussing") 14
onto it. So we want to replace "14 more than x" by
"x + 14". [Caution: we want to translate exactly,
so we should write "x + 14 and not "14 + x", because
we are starting with x and making it more. We are
not starting with 14.) So we now have:
6x is x + 14
6x is x + 14
Finally we replace the word "is" by " = "
6x = x + 14
6x = x + 14
That's the algebraic equation!
Edwin
(