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

1 Answer
Johnson Z.
Mar 13, 2016

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](useruploads.socratic.org)

:., x=-2 or 8.

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