Question

How do you solve `abs(2x-1)<9`?

Answer 1

See a solution process below:

Explanation:

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

`-9 < 2x - 1 < 9`

First, add `color(red)(1)` to each segment of the system of inequalities to isolate the `x` term while keeping the system balanced:

`-9 + color(red)(1) < 2x - 1 + color(red)(1) < 9 + color(red)(1)`

`-8 < 2x - 0 < 10`

`-8 < 2x < 10`

Now, divide each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`-8/color(red)(2) < (2x)/color(red)(2) < 10/color(red)(2)`

`-4 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 5`

`-4 < x < 5`

Or

`x > -4` and `x < 5`

Or, in interval notation:

`(-4, 5)`