A number is less than one fourth the sum of three times the number and four. What is the number?

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Answer 1 · 2017-09-19T00:43:38

The number is less than 4.

If we write the inequality out, we get this:

#x<1/4(3x+4)#

Now we just need to solve for x. Multiplying both sides by 4 yields:

#4x<3x+4#

Subtract 3x from both sides:
#x<4#

So any number less than 4 will work!

Answer 2 · 2017-09-19T00:49:03

n < 4

Writing the problem statement as an equation gives:

#n < 1/4(3n + 4)#

#n < 3/4n + 1#
...subtract #3/4n# from both sides:

#1/4n < 1#

muliply both sides by 4, gives:

#n < 4#

when possible, sanity check your work. For example, if n < 3, does that satisfy the inequality?

#1/4*(9+4) = 1/4(13) =3.25, and 3 is less than that. So, this checks.

How about 5? 5 should NOT satisfy the inequality.

#1/4(15+4) = 1/4(19) = 4.75, and 5 is greater than this, so this checks out too.