A number is less than one fourth the sum of three times the number and four. What is the number?
The number is less than 4.
If we write the inequality out, we get this:
Now we just need to solve for x. Multiplying both sides by 4 yields:
Subtract 3x from both sides:
So any number less than 4 will work!
n < 4
Writing the problem statement as an equation gives:
muliply both sides by 4, gives:
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.