How do you solve #-2| 7- x | \leq - 8#?

1 Answer
Jim G.
Jan 30, 2018

#3 <=x <=11#

Explanation:

#"divide both sides by "-2#

#rArrcancel(-2)/cancel(-2)|7-x|<= (-8)/(-2)#

#rArr|7-x|<=4#

#"inequalities of the type "|x|<= a#

#"always have solutions of the form "-a<= x <=a#

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

#"subtract 7 from each interval"#

#-4-7 <=cancel(7)cancel(-7)-x <=4-7#

#rArr-11 <=-x <=-3#

#"multiply each interval by "-1#

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

#rArr11>=x>=3#

#rArr3 <= x <=11#

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