Question

Solve for all values of x in simplest form 1+3|x-5|=10

Answer 1

`x=2,8`

Explanation:

So we have the equation:

`1+3|x-5|=10`

First, subtract 1 from both sides:

`3|x-5|=9`

Now, divide 3 from both sides:

`|x-5|=3`

Definition of absolute value:

`x-5=3\text{ or }x-5=-3`

For the left, add 5 to both sides.

For the right, add 5 to both sides:

`x=3+5\text{ or } x=-3+5\\x=8\text{ or }x=2`

Thus, the answers are:

`x=2,8`

Answer 2

x = 8 x = 2

Explanation:

1+3|x-5|=10

Subtract 1 from each side

1-1+3|x-5|=10-1

3|x-5|=9

Divide by 3

3/3|x-5|=9/3

|x-5|=3

There is a positive and negative solutions

x-5 =3 x-5 = -3

Add 5 to each side

x-5+5 = 3+5 x-5+5 = -3+5

x = 8 x = 2