First, subtract #color(red)(7/12)# from each side of the equation to solve for #m#:
#m + 7/12 - color(red)(7/12) = - 5/18 - color(red)(7/12)#
#m + 0 = - 5/18 - color(red)(7/12)#
#m = - 5/18 - color(red)(7/12)#
To add/subtract the two factions we need to get them over a common denominator:
#m = - (2/2 xx 5/18) - (3/3 xx color(red)(7/12))#
#m = -10/36 - 21/36#
#m = -31/36#
To check the solution, substitute #-31/36# for #m# in the original equation and calculate the result for both sides of the equation to ensure they are equal:
#m + 7/12 = -5/18# becomes:
#-31/36 + 7/12 = -5/18#
#-31/36 + (3/3 xx 7/12) = -5/18#
#-31/36 + 21/36 = -5/18#
#-10/36 = -5/18#
#-(2 xx 5)/(2 xx 18) = -5/18#
#-(color(red)(cancel(color(black)(2))) xx 5)/(color(red)(cancel(color(black)(2))) xx 18) = -5/18#
#-5/18 = -5/18#
Because both sides of the equation are equal the result checks out.
