Question

How do you solve `|x - 4| = 30`?

Answer 1

`x_1=34`
`x_2=-26`

Explanation:

For any modulus function/equation, we have two set of values, or branches:

`+x, x>=0`
`-x, x<0`

So we can write any modulus equation using these two branches:

`+(x-4)=30`
`x-4=30`
`x=34`

`-(x-4)=30`
`-x+4=30`
`-x=26`
`x=-26`

Answer 2

`x = 34` and `x = -26`

Explanation:

Because this is an absolute value problem we need to solve for both `+30` and `-30` as the term within the absolute value function will be positive regardless of whether it is a positive or negative result:

Solution 1)

`x - 4 = 30`

`x - 4 + 4 = 30 + 4`

`x - 0 = 34`

`x = 34`

Solution 2)

`x - 4 = - 30`

`x - 4 + 4 = -30 + 4`

`x - 0 = -26`

`x = -26`