# How do you write an absolute value equation that could be used to express the distance from point P to the origin is 5 more than twice the value of P?

Apr 3, 2015

The answer is: $\left\mid x \right\mid = 2 x + 5$

Given:

• $P$ is a point on the $x$-axis.

• The distance between the origin and $P$ is $5$ more than twice of the value of $P$

Absolute value operator gives us the distance from any point to the origin.

For example:

$\left\mid 5 \right\mid = \left\mid - 5 \right\mid = 5$

Lets say that $P$ is $\left(x , 0\right)$

The distance from point $P$ to origin is:

$\left(x , 0\right) - \left(0 , 0\right) = 2 x + 5$

$\left(x , 0\right) - \left(0 , 0\right) \equiv \left\mid P O \right\mid$

So the result is:

$\left\mid x \right\mid = 2 x + 5$