How do you solve and graph abs(x)>2?

Apr 3, 2017

Open circles at $+ 2$ and $- 2$ and a solid line going in two different directions one to the right at $+ 2$ and one to the left at $- 2$

Explanation:

Absolute value has both a positive and a negative value giving two inequalities

$+ x > 2$ and $- x > 2$

$+ x > 2$ can be graphed by making an open circle at $+ 2$ and an arrowed line going to the right

$- x > 2$ to solve this divide both sides and the inequality by $- 1$

$- \frac{x}{-} 1 = + x$

$\frac{2}{-} 1 = - 2$

$\frac{>}{-} 1 = <$ a greater than could be considered positive. A positive divided by a negative is a negative. < can be considered a negative

So $\frac{- x > 2}{- 1}$ is $+ x < - 2$

$x < - 2$ can be graphed with an empty circle at $- 2$ and an arrowed line going to the left.