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

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

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Answer 1 · 2016-03-13T07:00:15

$x = - 2, 8$ $x=-2,8$

Explanation:

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

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

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

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

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

$X X X X X x = \frac{10}{- 5} X X X X x - 3 x = - 24$ $color(white)(XXXXX)x=10/-5color(white)(XXXXx)-3x=-24$

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

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

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

1 Answer

Explanation:

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

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