SOLUTION: 2x-4/4 is less than or equal to 1+x/3

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Question 105220This question is from textbook
: 2x-4/4 is less than or equal to 1+x/3 This question is from textbook

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean like this,
%282x-4%29%2F4%3C=%281%2Bx%29%2F3
Multiply both sides by 3*4 to get rid of denominators.

3%282x-4%29%3C=4%281%2Bx%29
6x-12%3C=4%2B4x%29Distribute on both sides.
6x-4x-12%3C=4%2B4x-4x%29Additive inverse of 4x.
2x-12%3C=4
2x-12%2B12%3C=4%2B12Additive inverse of (-12).
2x%3C=16
2x%2F2%3C=16%2F2Multiplicative inverse of 2.
x%3C=8
Check your answer.
Let x=0, since x<8 then the equation should be true.
%282x-4%29%2F4%3C=%281%2Bx%29%2F3
%282%280%29-4%29%2F4%3C=%281%2B0%29%2F3
-1%3C=1%2F3
True statement, as you expected.
Let x=9, since x>9, then the equation should not be true.
%282%289%29-4%29%2F4%3C=%281%2B9%29%2F3
%2818-4%29%2F4%3C=10%2F3
3.5%3C=3.333
False statement, as you expected.
x%3C=8 Final answer.