How do you solve #|5x + 3| - 6\leq 5#?

1 Answer
Jim G.
Dec 11, 2017

#[-14/5,8/5]#

Explanation:

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

#"always have solutions of the form"#

#•color(white)(x)-a<=x<=a#

#|5x+3|-6<=5#

#"add 6 to both sides"#

#|5x+3|cancel(-6)cancel(+6)<=5+6#

#rArr|5x+3|<=11#

#rArr-11<=5x+3<=11#

#"subtract 3 from all 3 intervals"#

#-11-3<=5xcancel(+3)cancel(-3)<=11-3#

#rArr-14<=5x<=8#

#"divide all 3 intervals by 5"#

#rArr-14/5<=x<=8/5" is the solution"#

#"this can be expressed in "color(blue)"interval notation"#

#"using square brackets at each end "#

#rArrx in [-14/5,8/5]#

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