How do you solve #-3| a - 1| = - 15#?

2 Answers
Feb 25, 2018

Answer:

-4 and 6.

Explanation:

Start by isolating the absolute value (it contains the variable you're solving for, a.)

Dividing both sides by -3 we get |a-1| = 5

Then, split this into two parts:

#a-1 = 5#
and
#a-1 = -5#

Solve for a in both of those, and you should have your answers.

The reason we split it into two equations to remove the absolute value symbols is because those symbols make a negative number positive. If the variable inside is negative, it will be made positive. This must be reflected when we're solving an equation like this.

For example, #|-30| = 30#.
But #|30| = 30# too.
Now imagine if a variable a was in those bars.
#|a| = ? # The answer could be positive OR negative!

Hope this makes sense.

Feb 25, 2018

Answer:

#a=-4 " " " " \text{or} " " " " a=6#

are the required solutions.

# #
# #

Explanation:

#-3|a-1|=-15#

Divide both sides by #-3# to isolate the absolute value on the left hand side:

#\frac{-3|a-1|}{-3}=\frac{-15}{-3}#

Simplify:

#|a-1|=5#

# #

For an absolute value equation, there are two solutions.

#|f(a)|=a " " rightarrow " " f(a)=-a " " " " \text{or} " " " "f(a)=a#

# #

#a-1=-5 " " " " \text{or} " " " " a-1=5#

#a=-4 " " " " \text{or} " " " " a=6#

# #

That's it!