Question 189707
Is the equation {{{(x-7)/(x+2) = 1/4 }}} ???



{{{(x-7)/(x+2) = 1/4 }}} Start with the given equation.



{{{4(x-7) = 1(x+2)}}} Cross multiply



{{{4x-28=x+2}}} Distribute.



{{{4x=x+2+28}}} Add {{{28}}} to both sides.



{{{4x-x=2+28}}} Subtract {{{x}}} from both sides.



{{{3x=2+28}}} Combine like terms on the left side.



{{{3x=30}}} Combine like terms on the right side.



{{{x=(30)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=10}}} Reduce.



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Answer:


So the answer is {{{x=10}}} 





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OR...


Is the equation {{{x-7/(x+2) = 1/4}}} ????




{{{x-7/(x+2) = 1/4}}} Start with the given equation.



{{{4x(x+2)-4cross((x+2))(7/cross((x+2))) = cross(4)(x+2)(1/cross(4))}}} Multiply EVERY term by the LCD {{{4(x+2)}}} to clear the fractions.



{{{4x(x+2)-4(7)=x+2}}} Simplify



{{{4x(x+2)-28=x+2}}} Multiply



{{{4x^2+8x-28=x+2}}} Distribute



{{{4x^2+8x-28-x-2=0}}} Get everything to the left side



{{{4x^2+7x-30=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=4}}}, {{{b=7}}}, and {{{c=-30}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(7) +- sqrt( (7)^2-4(4)(-30) ))/(2(4))}}} Plug in  {{{a=4}}}, {{{b=7}}}, and {{{c=-30}}}



{{{x = (-7 +- sqrt( 49-4(4)(-30) ))/(2(4))}}} Square {{{7}}} to get {{{49}}}. 



{{{x = (-7 +- sqrt( 49--480 ))/(2(4))}}} Multiply {{{4(4)(-30)}}} to get {{{-480}}}



{{{x = (-7 +- sqrt( 49+480 ))/(2(4))}}} Rewrite {{{sqrt(49--480)}}} as {{{sqrt(49+480)}}}



{{{x = (-7 +- sqrt( 529 ))/(2(4))}}} Add {{{49}}} to {{{480}}} to get {{{529}}}



{{{x = (-7 +- sqrt( 529 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (-7 +- 23)/(8)}}} Take the square root of {{{529}}} to get {{{23}}}. 



{{{x = (-7 + 23)/(8)}}} or {{{x = (-7 - 23)/(8)}}} Break up the expression. 



{{{x = (16)/(8)}}} or {{{x =  (-30)/(8)}}} Combine like terms. 



{{{x = 2}}} or {{{x = -15/4}}} Simplify. 



So the answers are {{{x = 2}}} or {{{x = -15/4}}}




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OR...


Is the equation {{{(x-7)/x+2 = 1/4}}} ????



{{{(x-7)/x+2 = 1/4}}} Start with the given equation.



{{{4*cross(x)((x-7)/cross(x))+8x = cross(4)x(1/cross(4))}}} Multiply EVERY term by the LCD {{{4x}}} to clear the fractions. 



{{{4(x-7)+8x=x}}} Simplify



{{{4x-28+8x=x}}} Distribute.



{{{12x-28=x}}} Combine like terms on the left side.



{{{12x=x+28}}} Add {{{28}}} to both sides.



{{{12x-x=28}}} Subtract {{{x}}} from both sides.



{{{11x=28}}} Combine like terms on the left side.



{{{x=(28)/(11)}}} Divide both sides by {{{11}}} to isolate {{{x}}}.



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Answer:


So the answer is {{{x=28/11}}} which approximates to *[Tex \LARGE x \approx 2.545].