SOLUTION: Which of the following is true? A) The equation 3x=x has no solution. B)The solution to x/x-4=4/x-4 is x=4. C)There are two solutions for /3x-1/=9. D)Some linear equations can

Algebra ->  Linear-equations -> SOLUTION: Which of the following is true? A) The equation 3x=x has no solution. B)The solution to x/x-4=4/x-4 is x=4. C)There are two solutions for /3x-1/=9. D)Some linear equations can      Log On


   

Question 202031: Which of the following is true? A) The equation 3x=x has no solution. B)The solution to x/x-4=4/x-4 is x=4. C)There are two solutions for /3x-1/=9. D)Some linear equations can only be solved with a graphing utility. stumped. please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)

3x=x Start with the given equation.


3x-x=0 Subtract x from both sides.


2x=0 Combine like terms on the left side.


x=%280%29%2F%282%29 Divide both sides by 2 to isolate x.


x=0 Reduce.


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Answer:

So the solution is x=0


So the statement "The equation 3x=x has no solution" is false (since it does have a solution).




B)


x%2F%28x-4%29=4%2F%28x-4%29


4%2F%284-4%29=4%2F%284-4%29


4%2F0=4%2F0


Since division by zero is undefined, this means that x=4 CANNOT be a solution.

So the statement ")The solution to x/x-4=4/x-4 is x=4." is false.




C)




abs%283x-1%29=9 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

3x-1=-9 or 3x-1=9 Set the expression 3x-1 equal to the original value 9 and it's opposite -9




Now lets focus on the first equation 3x-1=-9


3x=-9%2B1Add 1 to both sides


3x=-8 Combine like terms on the right side


x=%28-8%29%2F%283%29 Divide both sides by 3 to isolate x



x=-8%2F3 Reduce


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Now lets focus on the second equation 3x-1=9



3x=9%2B1Add 1 to both sides


3x=10 Combine like terms on the right side


x=%2810%29%2F%283%29 Divide both sides by 3 to isolate x



x=10%2F3 Reduce





So the solutions to abs%283x-1%29=9 are:

x=-8%2F3 and x=10%2F3


Since there are two solutions, the statement "There are two solutions for /3x-1/=9" is true.




D)

Because you can solve ANY linear equation with a graph, I would argue that the statement "Some linear equations can only be solved with a graphing utility" is false. If the "some" was changed to "all", then it would true.


Note: I'm talking about approximate solutions. If the book means exact solutions, then the answer changes.