How do you solve and write the following in interval notation: #|6t-6|<6#?

1 Answer
Jan 9, 2017

Answer:

See full solution process below

Explanation:

Because this is a problem contain the absolute value function we must solve the problem for both the negative and positive forms of the problem or in this case +6 and -6.

Also, because it is an inequality we must solve it as a system of inequalities as shown below.

We can rewrite this problem as:

#-6 < 6t - 6 < 6#

We can now solve while ensuring we perform all operations to each portion of the system of inequalities.

First we will add #color(red)(6)# to each portion of the system:

#-6 + color(red)(6) < 6t - 6 + color(red)(6) < 6 + color(red)(6)#

#0 < 6t - 0 < 12#

#0 < 6t < 12#

Next we will divide each portion of the system by #color(red)(6)# to solve for #t# while keeping the system balanced:

#0/color(red)(6) < (6t)/color(red)(6) < 12/color(red)(6)#

#0 < (color(red)(cancel(color(black)(6)))t)/cancel(color(red)(6)) < 2#

#0 < t < 2#

Writing this solution in interval form gives:

(0, 2)