How do you solve #-6| m - 9| \geq - 72#?

1 Answer
smendyka
Dec 15, 2016

The solution is the range where #m# is: #-3 <= m <= 21#

Explanation:

First, we need to isolate the absolute value term. Additionally, when multiplying or dividing an inequality by a negative term the inequality reverses:

#(-6abs(m - 9))/-6<= -72/-6#

#(cancel(-6)abs(m - 9))/cancel(-6) <= 12#

#abs(m - 9) <= 12#

When solving an inequality for an absolute value you must solve a system of equation for positive and negative the result of the absolute value function:

#-12 <= m - 9 <= 12#

Now we solve for #m# while keeping the inequality system balanced:

#-12 + 9 <= m - 9 + 9 <= 12 + 9#

#-3 <= m - 0 <= 21#

#-3 <= m <= 21#

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