How do you solve #|-4x +7| = x + 17#?

1 Answer
Mar 13, 2016

Answer:

#x=-2,8#

Explanation:

#1#. Recall that the absolute value equality property, #|a|=b#, can be written as #a=+-b#. Thus, there will be two solutions.

#|-4x+7|=x+17color(white)(X),color(white)(X)"gives:"#

#-4x+7=x+17color(white)(XX)color(purple)("or")color(white)(XX)-4x+7=-(x+17)#

#2#. For each equation, solve for #x#.

#color(white)(XXXx)-5x=10color(white)(XX)color(purple)("or")color(white)(XX)-4x+7=-x-17#

#color(white)(XXXXX)x=10/-5color(white)(XXXXx)-3x=-24#

#color(white)(XXXx)color(green)(|bar(ul(color(white)(a/a)x=-2color(white)(a/a)|)))color(white)(XXXx)x=(-24)/(-3)#

#color(white)(XXXXXXXXXXXXxx)color(green)(|bar(ul(color(white)(a/a)x=8color(white)(a/a)|)))#

If you graph the equation, you can see that the intersection points occur when #x=-2# and #x=8#:

https://www.desmos.com/calculator/q61to1vgc3

#:.#, #x=-2# or #8#.