Question

How do you graph and solve `|5x – 2|>=8`?

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 write and solve this as:

`-8 >= 5x - 2 >= 8`

First, add `color(red)(2)` to each segment of the system of inequalities to isolate the `x` term while keeping the system balanced:

`-8 + color(red)(2) >= 5x - 2 + color(red)(2) >= 8 + color(red)(2)`

`-6 >= 5x - 0 >= 10`

`-6 >= 5x >= 10`

Now, divide each segment by `color(red)(5)` to solve for `x` while keeping the system balanced:

`-6/color(red)(5) >= (5x)/color(red)(5) >= 10/color(red)(5)`

`-6/5 >= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) >= 2`

`-6/5 >= x >= 2`

Or

`x <= -6/5`; `x >= 2`

Or

`(-oo, -6/5]`; `[2. +oo)`