Question

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

Answer 1

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<0`.

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+\frac13\right)=20\implies x+\frac13=5\implies\boxed{x=\frac{14}3}`

• On the other hand, if
  `x+\frac13<0`, then
  `\left|x+\frac13\right|=-\left(x+\frac13\right)`, so

`-4\left(x+\frac13\right)=20\implies x+\frac13=-5\implies\boxed{x=-\frac{16}3}`