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

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) (Show Source): You can put this solution on YOUR website!
A)

Start with the given equation.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is

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

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)

Start with the given equation

Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 9 and it's opposite -9

Now lets focus on the first equation

Add 1 to both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Reduce

-----------------------------------------

Now lets focus on the second equation

Add 1 to both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Reduce

So the solutions to are:

and

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.
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