Question

How do you graph and solve `abs (x -7) <=4`?

Answer 1

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Therefore we can rewrite this problem as a system of inequalities and solve it as:

`-4 <= x - 7 <= 4`

`-4 + color(red)(7) <= x - 7 + color(red)(7) <= 4 + color(red)(7)`

`3 <= x - 0 <= 11`

`3 <= x <= 11`

Or

`x >= 3`; `x <= 11`

Or, in interval notation:

`[3, 11]`