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?

1 Answer
Apr 3, 2015

The answer is: abs(x) = 2x+5|x|=2x+5

Given:

  • PP is a point on the xx-axis.

  • The distance between the origin and PP is 55 more than twice of the value of PP

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

For example:

abs(5) = abs(-5) = 5|5|=|5|=5

Lets say that PP is (x,0)(x,0)

The distance from point PP to origin is:

(x,0) - (0,0) = 2x+5(x,0)(0,0)=2x+5

(x,0) - (0,0) -= abs(PO)(x,0)(0,0)|PO|

So the result is:

abs(x) = 2x+5|x|=2x+5