How do you solve #|x - 7| <10#?

1 Answer
Jan 26, 2017

Answer:

See the entire solution process below:

Explanation:

To solve an absolute value inequality you must solve for both the negative and positive form of what the term within the absolute value function is compared to using a complex inequality.

#abs(x - 7) < 10->#

#-10 < x - 7 < 10#

Now, add #color(red)(7)# to each section of the complex inequality to solve for #x# while keeping the inequality balanced:

#-10 + color(red)(7) < x - 7 + color(red)(7) < 10 + color(red)(7)#

#-3 < x - 0 < 17#

#-3 < x < 17#

Or, in interval form:

(-3, 17)