Question 316855
It looks like your equation is:


{{{((1/4)*(x-3))+(5/6) = ((7/12)*x) + (2/3)}}}


Multiply both sides of this equation by 12 to get:


{{{12*(((1/4)*(x-3))+(5/6)) = 12*(((7/12)*x) + (2/3))}}}


Use the distributive law of multiplication to get:


{{{12*((1/4)*(x-3))+ 12*(5/6) = 12*(7/12)*x + 12*(2/3))}}}


Simplify this to get:


{{{3*(x-3) + 10 = 7*x + 8}}}


Use the distributive law of multiplication again to get:


{{{3*x - 9 + 10 = 7*x + 8}}}


Simplify this by combining like terms to get:


{{{3*x + 1 = 7x + 8}}}


Subtract 3*x from both sides of this equation and subtract 8 from both sides of this equation to get:


{{{-7 = 4*x}}}


this is the same as {{{4*x = -7}}}


Divide both sides of this equation by 4 to get:


{{{x = -7/4}}}


If the answer is correct, you should be able to substitute {{{-7/4}}} for x in the original equation and confirm that the equation is true.


The original equation is:


{{{((1/4)*(x-3))+5/6 = ((7/12)*x) + 2/3}}}


When x = (-7/4), this equation becomes:


{{{((1/4)*((-7/4)-3))+5/6 = ((7/12)*(-7/4)) + 2/3}}}


I used my calculator to solve and I got:


-.354166667 = -.354166667 which confirms that that value of x = -7/4 is good.