Question

How do you solve `|- 7x - 1| = 50`?

Answer 1

`x\in{-51/7; 7}`

Explanation:

We have:

`|-7x-1|=50`

If the absolute value of an expression is equal to a certain quantity, then the expression's value must either equal the quantity itself or its opposite. Therefore, we can deduce that:

`-7x-1\in{-50;50}`

`-(7x+1)\in{-50;50}`

Multiplying both sides by `-1`:

`7x+1\in{-50; 50}`

Subtracting `1` and dividing by `7`:

`x\in{(-50-1)/7;(50-1)/7}`

`x\in{-51/7; 7}`