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how to solve -5x + 8 less than or greater to x - 4

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2 Answers

-5x+8 vs x-4 
first, lets separate the 2 functions.
 
 
f(x) can be replaced by y 
 
f(x)= -5x+8
x=1 y=3
x=2 y=-2
x=3 y=-7
 
 
f(x)= x-4
x= 1 y=-3 
x=2 y=-2
x=3 y=-1
 
the equations intercept at 2,-2 
 
f(x)= x-4 is the greater equation if the linear equation is above the other equations plotted lines. 
 
Katie,
 
Are you confident that you read/wrote the question properly?  The phrase "...less than or greater to..." reminds me of something I might find in a line of computer code as some sort of Boolean operator, for example Pascal's 'not equal to' operator '<>'.

Comments

If that is indeed the sort of problem you are presenting, the approach requires the use of some Boolean logic.  Since the equations are being evaluated for non-equality as a true value, it is easiest to find the solutions which produce equality (a false Boolean value) in this case.  When is -5x + 8 equal to x - 4?
 
-5x + 8 = x - 4
 
Solve as any other equation in one variable....  I suggest adding 5x + 4 to both sides, thus:
 
-5x + 8 + 5x + 4 = x - 4 + 5x + 4
 
12 = 6x
 
And then dividing both sides by 6 (which, by the way, is clearly non-zero):
 
2 = x
 
We now have the only value of x where -5x + 8 is exactly equal to x - 4.  That then allows us to observe that for every x not equal to 2, -5x + 8 is not equal to x - 4.  At this point, one could even re-write the conditional statement as x <> 2, right?
Maybe better to write 2 <> x, so a typo doesn't accidentally make an assignment like in other languages.  :)

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