# How do you solve # abs(1 - 3b)= - 7#?

##### 2 Answers

This equation has no solutions.

#### Explanation:

We have to start with the definition of the absolute value.

The absolute value of a non-negative number is this number itself.

Absolute value of the negative number is its negation.

In mathematical symbol it looks like that:

Using this definition, let's divide a set of all possible values of

(a) those where

(b) those where

In case (a) our equation looks like this:

which has a solution

This solution does not belong to the area of

In case (b) our equation looks like this:

which has a solution

This solution does not belong to the area of

So, no solutions are found for this equation.

We can confirm this graphically by observing that function

graph{|1-3x|+7 [-46.23, 46.25, -23.12, 23.1]}

exactly no solutions

#### Explanation:

because

you can't find any solution which satifies this equation