# How do you solve abs(k-5)=4?

Aug 21, 2017

Given: $\left\mid k - 5 \right\mid = 4$

You can break the above equation into two equations without the absolute value function, one where the right side is positive, and the other where the right side is negative:

$k - 5 = 4 \mathmr{and} k - 5 = - 4$

Add 5 to both sides of both equations:

$k = 9 \mathmr{and} k = 1$

Check $k = 9$

$| 9 - 5 | = 4$

$| 4 | = 4$

$4 = 4$

Check k = 1:

$| 1 - 5 | = 4$

$| - 4 | = 4$

$4 = 4$

Both values check.