Question

How do you solve `|10x + -8| <28`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite the inequality as:

`abs(10x - 8) < 28`

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

`-28 < 10x - 8 < 28`

`-28 + color(red)(8) < 10x - 8 + color(red)(8) < 28 + color(red)(8)`

`-20 < 10x - 0 < 36`

`-20 < 10x < 36`

`-20/color(red)(10) < (10x)/color(red)(10) < 36/color(red)(10)`

`-2 < (color(red)(cancel(color(black)(10)))x)/cancel(color(red)(10)) < 3.6`

`-2 < x < 3.6`

Or

`x > -2` and `x < 3.6`

Or, in interval notation

`(-2, 3.6)`