First, convert the two mixed numbers to improper fractions:
#-5x - 5 1/4 = -16 3/4#
#-5x - (5 + 1/4) = -(16 + 3/4)#
#-5x - ([4/4 xx 5] + 1/4) = -([4/4 xx 16] + 3/4)#
#-5x - (20/4 + 1/4) = -([64/4 + 3/4)#
#-5x - (20 +1)/4 = -(64 + 3)/4#
#-5x - 21/4 = -67/4#
Next, add #color(red)(21/4)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#-5x - 21/4 + color(red)(21/4) = -67/4 + color(red)(21/4)#
#-5x - 0 = (-67 + color(red)(21))/4#
#-5x = -46/4#
#-5x = -(23 xx 2)/(2 xx 2)#
#-5x = -(23 xx color(red)(cancel(color(black)(2))))/(2 xx color(red)(cancel(color(black)(2))))#
#-5x = -23/2#
Then, multiply each side of the equation by #color(red)(-1/5)# to solve for #x# while keeping the equation balanced.
#-5x xx color(red)(-1/5) = -23/2 xx color(red)(-1/5)#
#-color(red)(cancel(color(black)(5)))x xx color(red)(-1/color(black)(cancel(color(red)(5)))) = 23/10#
#-x xx -1 = 23/10#
#x = 23/10#
If necessary, we can convert the result to a mixed number:
#x = (20 + 3)/10#
#x = 20/10 + 3/10#
#x = 2 + 3/10#
#x = 2 3/10#
