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Fed [463]
3 years ago
12

Solve the equation and show all work. 4|x + 1/3| = 20 i'm kind of stuck hhh

Mathematics
1 answer:
34kurt3 years ago
6 0

Absolute value is a function that takes some number and outputs the size of that number, regardless of the sign. By definition, |x|=x if x\ge0, and |x|=-x if x.

For example,

  • |2| = 2 because the input 2 is positive, so the input is unchanged;
  • |-3| = -(-3) = 3 because the input -3 is negative, so the sign is switched.

What this means for this problem is that there are two cases to consider:

  • If x+\frac13\ge0, then \left|x+\frac13\right|=x+\frac13, so that

4\left(x+\dfrac13\right)=20\implies x+\dfrac13=5\implies\boxed{x=\dfrac{14}3}

  • On the other hand, if x+\frac13, then \left|x+\frac13\right|=-\left(x+\frac13\right), so

-4\left(x+\dfrac13\right)=20\implies x+\dfrac13=-5\implies\boxed{x=-\dfrac{16}3}

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