How do you graph and solve #abs (x -7) <=4#?

1 Answer
Jul 30, 2018

Answer:

See a solution process below:

Explanation:

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.

Therefore we can rewrite this problem as a system of inequalities and solve it as:

#-4 <= x - 7 <= 4#

#-4 + color(red)(7) <= x - 7 + color(red)(7) <= 4 + color(red)(7)#

#3 <= x - 0 <= 11#

#3 <= x <= 11#

Or

#x >= 3#; #x <= 11#

Or, in interval notation:

#[3, 11]#