The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
Thus the modulus function is defined as,
#f(x) = |x| = x, x>=0#
#f(x) = |x| = -x, x<0#
Solution 1:
#10r - 9 = -99#
#10r - 9 + color(red)(9) = -99 + color(red)(9)#
#10r - 0 = -90#
#10r = -90#
#(10r)/color(red)(10) = -90/color(red)(10)#
#(color(red)(cancel(color(black)(10)))r)/cancel(color(red)(10)) = -9#
#r = -9#
Solution 2:
#10r - 9 = 99#
#10r - 9 + color(red)(9) = 99 + color(red)(9)#
#10r - 0 = 108#
#10r = 108#
#(10r)/color(red)(10) = 108/color(red)(10)#
#(color(red)(cancel(color(black)(10)))r)/cancel(color(red)(10)) = (2 xx 54)/(2 xx 5)#
#r = (color(red)(cancel(color(black)(2))) xx 54)/(color(red)(cancel(color(black)(2))) xx 5)#
#r = 54/5#
The Solutions Are: #r = -9# and #r = 54/5#
