How do you solve #|\frac { x } { 5} | - 10< - 8#?

1 Answer
smendyka
Aug 13, 2017

See a solution process below:

Explanation:

First, add #color(red)(10)# to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

#abs(x/5) - 10 + color(red)(10) < -8 + color(red)(10)#

#abs(x/5) - 0 < 2#

#abs(x/5) < 2#

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.

#-2 < x/5 < 2#

#color(red)(5) * -2 < color(red)(5) * x/5 < color(red)(5) * 2#

#-10 < cancel(color(red)(5)) * x/color(red)(cancel(color(black)(5))) < 10#

#-10 < x < 10#

Or

#x > -10# and #x < 10#

Or, in interval notation:

#(-10, 10)#

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