How to solve this absolute value inequality? $ |x| + |x - 2| \gt 5 $ I'm not sure how to solve this inequality. Can someone please explain step-by-step? Thanks!

$ |x| + |x - 2| \gt 5 $
If $x \geq 2$, then $|x| + |x-2| = 2x-2$, which is $ &gt; 5$ iff $x &gt; \frac{7}{2}$.
If $0 \leq x &lt; 2$, then $|x| + |x-2| = x+2-x = 2 &lt; 5$. If $x &lt; 0$, then $|x| + |x-2| = -x+2-x = 2-2x$, which is $&gt; 5$ iff $x &lt; \frac{-3}{2}$.

Do you then know how to conclude?
Since $\mid x\mid$ and $\mid{x-2}\mid$ will always be positive, you can change the equation to $x+x-2 \gt 5$. This gives you $2x-2\gt 5$ 
then  $2x \gt 7$ and the final answer is $x \gt \frac72$
Also since x can be negative you must set another equation as $|x|+|x-2| \lt -5$ and solve this as $x+x-2 \lt -5$ and get $2x-2 \lt -5$ then $2x \lt -3$ then $x \lt -\frac{3}{2}$ so $x \gt \frac72$ or $x \lt -\frac{3}{2}$