Twelve less than four times a number is the same as six times the number. How do you find the number?

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Answer 1 · 2017-05-10T22:52:17

See a solution process below:

First, let's call the number we are looking for: #n#

Then:

"four times a number" can be written as #4n#

"Twelve less than" this would be written as #4n - 12#

"is the same as" gives us an equal sign: #4n - 12 = #

And "six times the number" finalizes the equation as:

#4n - 12 = 6n#

Next, subtract #color(red)(4n)# from each side of the equation to isolate the #n# term while keeping the equation balanced:

#-color(red)(4n) + 4n - 12 = -color(red)(4n) + 6n#

#0 - 12 = (-color(red)(4) + 6)n#

#-12 = 2n#

Now, divide each side of the equation by #color(red)(2)# to solve for #n# while keeping the equation balanced:

#-12/color(red)(2) = (2n)/color(red)(2)#

#-6 = (color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2))#

#-6 = n#

#n = -6#