# LINR 2 | Lesson 1 | Explore Absolute Value Solutions

1. Since $$|x | = 5$$ means that the distance of $$x$$ is 5 units from zero, then $$x=-5$$ and $$x= 5$$
2. Since $$|x-3| = 5$$  means that the quantity of $$(x-3)$$ is 5 units from zero, then $$(x-3)= 5$$ or $$(x-3) = -5$$. Solving each equation, we find that $$x = 8$$ or $$x = -2$$
3. $$|2x-3| = 5$$ means that $$(2x-3 )= 5$$ or $$(2x-3) = -5$$. Solving each equation, we find that $$x = 4$$ or $$x = -1$$
4. $$|x | = -5$$ means that the distance from zero is $$-5$$, but distance is always positive therefore there is no solution.

Go back to Try This!