SOLUTION: I have this problem and I want to know if I did it correct? 4-x/x-2=-2/x-2, this is how I worked I tried to work the problem out, the -2&-2 cancel each other out and then it left 4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have this problem and I want to know if I did it correct? 4-x/x-2=-2/x-2, this is how I worked I tried to work the problem out, the -2&-2 cancel each other out and then it left 4      Log On


   

Question 163753: I have this problem and I want to know if I did it correct? 4-x/x-2=-2/x-2, this is how I worked I tried to work the problem out, the -2&-2 cancel each other out and then it left 4-x/x=x-2, then add +2 to both sides 4+2=6 and x-2+2 cancels out each other x=6. Is this the correct answer or can it be answered?
But I have a couple of other problems that I need help with.1/4=3-2x-1 over x+2, x3/2=125 and x+20-x=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Your first problem is ambiguous (ie not clear). Is the equation %284-x%29%2F%28x-2%29=-2%2F%28x-2%29 ???

Use parenthesis to be very clear which terms are the numerator and which are the denominator.


If the equation is %284-x%29%2F%28x-2%29=-2%2F%28x-2%29, then you are correct. The answer is x=6. You can verify by substituting and simplifying.



# 2

Is the equation 1%2F4=3-%282x-1%29%2F%28x%2B2%29 ???


1%2F4=3-%282x-1%29%2F%28x%2B2%29 Start with the given equation


Multiply EVERY term by the LCD 4%28x%2B2%29 to clear the fractions


1%28x%2B2%29=3%284%28x%2B2%29%29-4%282x-1%29 Multiply and simplify


1%28x%2B2%29=12%28x%2B2%29-4%282x-1%29 Multiply


x%2B2=12x%2B24-8x%2B4 Distribute.


x%2B2=4x%2B28 Combine like terms on the right side.


x=4x%2B28-2 Subtract 2 from both sides.


x-4x=28-2 Subtract 4x from both sides.


-3x=28-2 Combine like terms on the left side.


-3x=26 Combine like terms on the right side.


x=%2826%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=-26%2F3 Reduce.


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Answer:

So the answer is x=-26%2F3 which approximates to x=-8.667.





# 3

The equation x3/2=125 is missing a sign or operator (like + or *)





# 4



x%2B20-x=0 Start with the given equation.


0x%2B20=0 Combine like terms on the left side.


0x=0-20 Subtract 20 from both sides.


0x=-20 Combine like terms on the right side.


0=-20 Simplify.


Since this equation is never true for any x value, this means that there are no solutions.