Question 6766
(x)/(180)-x=(1)/(8)


Find the LCD (least common denominator) of (x)/(180)-x+(1)/(8).


Least common denominator: 360

Multiply each term in the equation by 360 in order to remove all the 

denominators from the equation.

(x)/(180)*360-x*360=(1)/(8)*360

Cancel the common factor of 180 in the denominator of the first term (x)/(180)


and the second term 360.


(x)/(<X>180<x>)*<X>360<x>^(2)-x*360=(1)/(8)*360


Reduce the expression by removing the common factor of 180 in the denominator 

of the first term (x)/(180) and the second term 360.


x*2-x*360=(1)/(8)*360


Multiply x by 2 to get 2x.


2x-x*360=(1)/(8)*360



Multiply -x by 360 to get -360x.


2x-360x=(1)/(8)*360


According to the distributive property, for any numbers a, b, and c, 


a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both 2x and -360x.


(2-360)x=(1)/(8)*360


To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value.  In this example, subtract the absolute values of 2 and -360 and give the result the same sign as the integer with the greater absolute value.


(-358)x=(1)/(8)*360



Remove the parentheses.


-358x=(1)/(8)*360


Cancel the common factor of 8 in the denominator of the first term (1)/(8) and the second term 360.


-358x=(1)/(<X>8<x>)*<X>360<x>^(45)


Reduce the expression by removing the common factor of 8 in the denominator of the first term (1)/(8) and the second term 360.


-358x=1*45


Multiply 1 by 45 to get 45.


-358x=45


Divide each term in the equation by -358.


-(358x)/(-358)=(45)/(-358)


Move the minus sign from the denominator to the front of the expression


-(-(358x)/(358))=(45)/(-358)


Cancel the common factor of 358 in -(358x)/(358).


-(-(<X>358<x>x)/(<X>358<x>))=(45)/(-358)


Remove the common factors that were cancelled out.


-(-x)=(45)/(-358)


Multiply - by the -x inside the parentheses.


-*-x=(45)/(-358)


Multiply - by -x to get x.


x=(45)/(-358)


Move the minus sign from the denominator to the front of the expression.


x=-((45)/(358))


Multiply -1 by the (45)/(358) inside the parentheses.


Answer is:
x=-(45)/(358)