How do you solve the inequality #abs(4-x)<=8#?
1 Answer
Feb 7, 2018
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#
