Question

How do you solve `|- 2d | \leq 12`?

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.

`-12 <= -2d <= 12`

Divide each segment of the system of inequalities by `color(blue)(-2)` to solve for `d` while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:

`(-12)/color(blue)(-2) color(red)(>=) (-2d)/color(blue)(-2) color(red)(>=) 12/color(blue)(-2)`

`6 color(red)(>=) (color(blue)(cancel(color(black)(-2)))d)/cancel(color(blue)(-2)) color(red)(>=) -6`

`6 color(red)(>=) d color(red)(>=) -6`

Or

`d >= -6` and `d <= 6`

Or. in interval notation:

`[-6, 6]`