First, subtract #color(red)(2)# from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:
#-color(red)(2) + 2 + abs(-6b) > -color(red)(2) + 62#
#0 + abs(-6b) > 60#
#abs(-6b) > 60#
The absolute value function takes any number and converts it to its non-negative form. Therefore, to solve for an absolute value you must solve the term within the absolute value for both its positive and negative equivalent.
#-60 > -6b > 60#
Now, divide each segment of the system of inequalities by #color(blue)(-6)# to solve for #b# while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operators:
#(-60)/color(blue)(-6) color(red)(<) (-6b)/color(blue)(-6) color(red)(<) (60)/color(blue)(-6)#
#10 color(red)(<) (color(blue)(cancel(color(black)(-6)))b)/cancel(color(blue)(-6)) color(red)(<) -10#
#10 color(red)(<) b color(red)(<) -10#
Or
#b > 10# and #b < -10#
Or, in interval notation:
#(-oo, -10)# and #(10, +oo)#
