How do you solve the inequality #abs(4-x)<=8#?

1 Answer
Feb 7, 2018

Answer:

#-4<=x<=12#

Explanation:

#"inequalities of the type "|x|<=a" always have solutions"#
#"of the form"#

#-a<=x<=a#

#rArr|4-x|<=8" will have solutions"#

#-8 <= 4-x <= 8#

#"to isolate the x term in the middle subtract 4 from "#
#"each interval"#

#-8color(red)(-4)<=4color(red)(-4)-x <=8color(red)(-4)#

#rArr-12 <=- x <=4#

#"multiply each interval by "-1#

#"remembering to "color(red)"reverse the inequality signs"#

#rArr12 >=x>=-4#

#rArr-4 <=x <=12#