SOLUTION: When 8 is subtracted from the sum of three times a number and 6, the result is less than 4 more than the number. Find the numbers.

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Question 1203407: When 8 is subtracted from the sum of three times a number and 6, the result is less than 4 more than the number. Find the numbers.
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Follow your description literally as expressed and solve. Simple reading comprehension!


-8%2B3n%2B6%3C4%2Bn
3n-2%3Cn%2B4
2n%3C6
n%3C3-------------------the number is less than 3.

Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.

Somebody exercises in creating the most twisted sentence.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = some unknown number
3x = three times that number
3x+6 = add on 6

So far we've addressed the "sum of three times a number and 6" portion.

The next thing we'll do is subtract off 8 to get (3x+6)-8 which simplifies to 3x-2

This result (3x-2) is less than 4 more than the number. So it is less than x+4

3x-2 < x+4
3x-x < 4+2
2x < 6
x < 6/2
x < 3

The set of solutions is anything smaller than 3.
Some example solutions:
x = 2
x = 1.57123
x = 1
x = 0.4
x = 0
x = -22
There are infinitely many solutions.

Non-solutions would be:
x = 3
x = 4
x = 5
x = 9
There are infinitely many non-solutions.

The number line graph of x < 3 has an open circle at 3 with shading to the left.
The open circle means "exclude this endpoint from the solution set".