solve the inequations and provide the solutions in brackets I have 2 inequations which I solve, but when I compare the result with websites like wolframalpha I get different results. 
$|2-x|+|2+x| \leq 10$
I continue with $2-x+2-x\leq10$ OR $2-x+2-x\geq-10$ 
and I get the results $x\geq3$ and $x\leq7 $
$|6-4x|\geq|x-2|$
$6-4x \geq x-2$ OR $6-4x \leq -x+2 $
and I get $x\leq8/5$ and $x\geq4/3$
Are my results correct or not? 
Thank you

You are wrong because you don't manage correctly the sign of the expressions in the absolute values.
In your first inequality you have $ 2-x\ge 0 \iff x\le 2$ and $2+x \ge 0 \iff x\ge -2$. So the inequality  reduces to three systems:
$$
\begin{cases}
x<-2\\
2-x-2-x\le 10
\end{cases}
\lor
\begin{cases}
-2\le x<2\\
2-x+2+x\le 10
\end{cases}
\lor
\begin{cases}
x\ge 2\\
x-2+2+x\le 10
\end{cases}
$$
look well at these systems and understand where they come from, than solve  and find the solution $-5\le x\le 5$ or, in brakets; $[-5,5]$.
Than use the same method for the other inequality.
