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6|3x -1|+4=2|x+8|-8

Pls help quick

User Polemon
by
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1 Answer

4 votes

Answer:

x = 1/10 or x = 5/8

Explanation:

You want the solutions to the absolute value equation ...

6|3x -1| +4 = 2|x +8| -8

Simplify

Subtracting the right side expression, we have ...

6|3x -1| +4 -2|x +8| +8 = 0

3|3x -1| -|x +8| +6 = 0 . . . . . . . divide by 2

Domain

The two absolute value functions divide the domain of the expression into three parts. The boundaries of these domains are ...

3x -1 = 0 ⇒ x = 1/3

x +8 = 0 ⇒ x = -8

x ≥ 1/3

In this domain, both absolute value expressions do nothing, as their arguments are both positive.

3(3x -1) -(x +8) +6 = 0

9x -3 -x -8 +6 = 0

8x -5 = 0

x = 5/8 . . . . . one solution to the equation

-8 ≤ x ≤ 1/3

In this domain, the left absolute value expression has a negative argument, so the equation becomes ...

-3(3x -1) -(x +8) +6 = 0

-9x +3 -x -8 +6 = 0

-10x +1 = 0

x = 1/10 . . . . . . another solution to the equation

x < -8

In this domain, both absolute value expressions have negative arguments, so the equation becomes ...

-3(3x -1) +(x +8) +6 = 0

-9x +3 +x +8 +6 = 0

-8x +17 = 0

x = 17/8 . . . . . . . . not in the domain, not a solution

The solutions are x = 1/10 or x = 5/8.

__

Additional comment

A graphing calculator often finds zeros easily, so we find it convenient to write the equation in a form that evaluates to zero at the solution points. That is what we have done above and in the attachment.

<95141404393>

6|3x -1|+4=2|x+8|-8 Pls help quick-example-1
User Jon Spokes
by
7.4k points

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