Question

How do you solve `|x - 7| <10`?

Answer 1

See the entire solution process below:

Explanation:

To solve an absolute value inequality you must solve for both the negative and positive form of what the term within the absolute value function is compared to using a complex inequality.

`abs(x - 7) < 10->`

`-10 < x - 7 < 10`

Now, add `color(red)(7)` to each section of the complex inequality to solve for `x` while keeping the inequality balanced:

`-10 + color(red)(7) < x - 7 + color(red)(7) < 10 + color(red)(7)`

`-3 < x - 0 < 17`

`-3 < x < 17`

Or, in interval form:

(-3, 17)