7 Times a number equals 3 less than 5 times that number. What is the number?

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Answer 1 · 2017-01-11T23:23:37

The number is #-3/2#

First, let's define the number we are looking for as #n#.

In mathematical terms "7 times as number" can be written as:

#7 xx n# or #7 * n# or we will use #7n#

In mathematical terms "3 less than 5 times that number" can be written as:

#5n - 3#

If these two expressions are equal we can write:

#7n = 5n - 3#

We can now solve for #n#:

#7n - color(red)(5n) = 5n - 3 - color(red)(5n)#

#(7 - 5)n = 5n - color(red)(5n) - 3#

#2n = 0 - 3#

#2n = -3#

#(2n)/color(red)(2) = -3/color(red)(2)#

#(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = -3/2#

#n = -3/2#