How do you solve $abs(x-3)-6=2$ ?

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How do you solve $abs(x-3)-6=2$ ?

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Answer 1 · 2018-03-14T22:56:50

See a solution process below:

Explanation:

First, add $color(red)(6)$ to each side of the equation to isolate the absolute value function while keeping the equation balanced:

$abs(x - 3) - 6 + color(red)(6) = 2 + color(red)(6)$

$abs(x - 3) - 0 = 8$

$abs(x - 3) = 8$

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

$x - 3 = -8$

$x - 3 + color(red)(3) = -8 + color(red)(3)$

$x - 0 = -5$

$x = -5$

Solution 2:

$x - 3 = 8$

$x - 3 + color(red)(3) = 8 + color(red)(3)$

$x - 0 = 11$

$x = 11$

The Solution Set Is:

#x = {-5, 11}

Answer 2 · 2018-03-14T22:57:37

${x-3>0$
${-x+3>0$

So it's either $x-3$ or $-x+3$ and you put both of these separate

$x-3-6=2$ from where $x=11$

and

$-x+3-6=2$ from where $x=-5$

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How do you solve $abs(x-3)-6=2$ ?

2 Answers

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