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Question 652700: I need to solve the following inequality and i've tried everything but i can't seem to find an answer.
The problem says:
A number is less than one fourth the sum of three times the number and four.
x < 1/4 + 3x + 4
Found 3 solutions by ewatrrr, Shana-D77, DrBeeee:
Answer by ewatrrr(24785)   (Show Source):
Answer by Shana-D77(132)  (Show Source):
You can put this solution on YOUR website! You almost got it, but there's a problem:
"one fourth the sum of three times the number and four" is implying multiplication. "one-fourth the sum" is "one-fourth OF the sum". OF means multiply. So we have:
x < 1/4(3x + 4)
4x < 3x + 4 (multiplied both sides by 4 to get rid of 1/4)
x < 4 (subtracted 3x from both sides)
Answer by DrBeeee(684)  (Show Source):
You can put this solution on YOUR website! The expession does not satify the statement,"One fourth of ...", it should be
(1) x < (1/4)*(3x+4), where you multiply instead of add. Of means multiply.
Now solve (1) for x.
Multiply both sides by 4 and get
(2) 4x < 3x + 4 or
(3) x < 4
Let's check our answer using (1) and x = 4-d, where d is an incrementally small positive value (almost zero), such that d>0, making x < 4
Is (4-d < (1/4)*(3*(4-d) + 4)?
Is (4-d < (1/4)*(12 - 3d +4)?
Is (4-d < (1/4)*(16-3d)?
Is (4-d < 4 - (3/4)d)?
Is ( -d < -(3/4)d)? or, since d>0
Is ( -1 < -(3/4))? Yes.
Answer: The real number x is less than 4.
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