Question

How do you solve `|-.05x|>1`?

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.

We can therefore rewrite and solve this problem without the absolute value function as:

`-1 > -0.05x > 1`

We can divide each segment of the system of inequalities but `color(blue)(-0.05)` to solve for `x` while keeping the system balanced.

However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operators:

`-1/color(blue)(-0.05) color(red)(<) (-0.05x)/color(blue)(-0.05) color(red)(<) 1/color(blue)(-0.05)`

`20 color(red)(<) (color(blue)(cancel(color(black)(-0.05)))x)/cancel(color(blue)(-0.05)) color(red)(<) -20`

`20 color(red)(<) x color(red)(<) -20`

Or

`x < -20`; `x > 20`

Or, in interval notation

`(-oo, -20)`; `(20, +oo))`