Question

How do you graph and solve `| 5x - 1 | <= 14`?

Answer 1

`"See the Explanation"`

Explanation:

`|5x−1|≤14`

This means the distance from 5x - 1 to zero must be less than or equal to 14.
It can be rewritten as `-14 ≤ 5x−1 ≤14`

So, draw `y = -14` and `y = 14`, and `5x - 1`.
The answer is where the line 5x - 1 is in between -14 and 14 like the plot below:
https://www.desmos.com/calculator/psnq5dutum

And here we find the answer without graphing:
`-14 ≤ 5x−1 ≤14`
`-14 + 1≤ 5x ≤14+1`
`-13≤ 5x ≤15`
`-13/5≤ x ≤15/5`
`-2.6≤ x ≤3`

The answer is `[-2.6, 3]`