Question

How do you solve `|3x - 5|+ 4= 1`?

Answer 1

No solutions.

Explanation:

`|3x - 5| + 4 = 1`

First, we need to make the value in the absolute value by itself. So subtract `4` from both sides of the equation:
`|3x - 5| = -3`

Now, we set the value inside the absolute value equal to the other side, and the opposite of the other side.

So we do:
`3x - 5 = -3` AND `3x - 5 = 3`

`3x = 2` `quadquadquadquadquadquad` AND `quadquadquadquad3x = 8`

`x = 2/3` `quadquadquadquadquadquad` AND `quadquadquadquadquadx = 8/3`

`x = 2/3,` `8/3`

However, we need to check our solutions and see if they really work by plugging them in to the original equation:
`|3x-5| + 4= 1`

`|3x - 5| = -3`

Instead of plugging in the solutions, we can actually see that an absolute value CANNOT equal to a negative number, so the answer is actually no solution.

Hope this helps!