Question

Question #e47ea

Answer 1

See the entire 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.

`-3 < 1 - 2x < 3`

`-color(red)(1) - 3 < -color(red)(1) + 1 - 2x < -color(red)(1) + 3`

`-4 < 0 - 2x < 2`

`-4 < -2x < 2`

Because we are going to divide or multiply by a negative term we must reverse the inequality operators:

`(-4)/color(red)(-2) color(blue)(>) (-2x)/color(red)(-2) color(blue)(>) 2/color(red)(-2)`

`2 color(blue)(>) (color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) color(blue)(>) -1`

`2 > x > -1`