How do you graph and solve #|5-x| +5>=5#?

1 Answer
Aug 27, 2017

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(5)# from each side of the inequality to isolate the absolute value function:

#abs(5 - x) + 5 - color(red)(5) >= 5 - color(red)(5)#

#abs(5 - x) + 0 >= 0#

#abs(5 - x) >= 0#

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.

#-0 >= 5 - x >= 0#

#0 >= 5 - x >= 0#

#-color(red)(5) + 0 >= -color(red)(5) + 5 - x >= -color(red)(5) + 0#

#-5 >= 0 - x >= -5#

#-5 >= -x >= -5#

#color(bue)(-1) xx -5 color(red)(<=) color(bue)(-1) xx -x color(red)(<=) color(bue)(-1) xx -5#

#5 color(red)(<=) x color(red)(<=) 5#

Or

#x >= 5# and #x <= 5#

Because #x# can be greater than or less than #5# and it can be equal to #5# the solution is #x# is the set of all Real Numbers: #{RR}#.

In other words, #x# can be any value and the inequality will be true.

The graph will look like a solid shaded area:

graph{x>=-10005}