Question 163753
# 1


Your first problem is ambiguous (ie not clear). Is the equation {{{(4-x)/(x-2)=-2/(x-2)}}} ??? 


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



If the equation is {{{(4-x)/(x-2)=-2/(x-2)}}}, then you are correct. The answer is {{{x=6}}}. You can verify by substituting and simplifying.


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# 2


Is the equation {{{1/4=3-(2x-1)/(x+2)}}} ???



{{{1/4=3-(2x-1)/(x+2)}}} Start with the given equation



{{{(cross(4)(x+2))(1/cross(4))=3(4(x+2))-(4cross(x+2))((2x-1)/cross(x+2))}}} Multiply EVERY term by the LCD {{{4(x+2)}}} to clear the fractions



{{{1(x+2)=3(4(x+2))-4(2x-1)}}} Multiply and simplify



{{{1(x+2)=12(x+2)-4(2x-1)}}} Multiply



{{{x+2=12x+24-8x+4}}} Distribute.



{{{x+2=4x+28}}} Combine like terms on the right side.



{{{x=4x+28-2}}} 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=(26)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{x}}}.



{{{x=-26/3}}} Reduce.



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Answer:


So the answer is {{{x=-26/3}}} which approximates to {{{x=-8.667}}}. 




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# 3


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



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# 4




{{{x+20-x=0}}} Start with the given equation.



{{{0x+20=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 <font size=4><b>never</b></font> true for any x value, this means that there are no solutions.