How to add two signals?
First express $x(t)$ in piece-wise form:

$$
x(t) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; t  &lt; -2 \\
0.5(t+2) &amp;, \text{ for}  &amp;-2 &lt; t &lt; 0 \\
-t+1 &amp;, \text{ for}  &amp; 0 &lt; t &lt; 1 \\
0 &amp;, \text{ for }   &amp;1 &lt; t \\
\end{cases}
$$

Now, express $x_1(t)=x(2t)$ in a similar form: 
$$
x_1(t) = x(2t) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; 2t  &lt; -2 \\
0.5(2t+2) &amp;, \text{ for}  &amp;-2 &lt; 2t &lt; 0 \\
-2t+1 &amp;, \text{ for}  &amp; 0 &lt; 2t &lt; 1 \\
0 &amp;, \text{ for }   &amp;1 &lt; 2t \\
\end{cases}
$$

Recognize how the formula and intervals are adjusted for $x_1(t)$
$$
x_1(t) = x(2t) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; t  &lt; -1 \\
t+1 &amp;, \text{ for}  &amp;-1 &lt; t &lt; 0 \\
-2t+1 &amp;, \text{ for}  &amp; 0 &lt; t &lt; 0.5 \\
0 &amp;, \text{ for }   &amp;0.5 &lt; t \\
\end{cases}
$$

Now, express $x_2(t)=x(2t+2)$ in a similar form: 
$$
x_2(t) = x(2t+2) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; 2t+2  &lt; -2 \\
0.5(2t+2+2) &amp;, \text{ for}  &amp;-2 &lt; 2t+2 &lt; 0 \\
-(2t+2)+1 &amp;, \text{ for}  &amp; 0 &lt; 2t+2 &lt; 1 \\
0 &amp;, \text{ for }   &amp;1 &lt; 2t+2 \\
\end{cases}
$$

Recognize how the formula and intervals are adjusted for $x_2(t)$ as well
$$
x_2(t) = x(2t+2) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; t &lt; -2 \\
t+2 &amp;, \text{ for}  &amp;-2 &lt; t &lt; -1 \\
-2t-1 &amp;, \text{ for}  &amp; -1 &lt; t &lt; -.50 \\
0 &amp;, \text{ for }   &amp;-0.5 &lt; t \\
\end{cases}
$$

Now add those two piecewise defined signals $x_1(t)$ and $x_2(t)$, considering the intervals carefully:

$$ y(t) = x_1(t) + x_2(t) = x(2t) + x(2t + 2) =
\begin{cases}
0 ~&amp;,  \text{ for}  &amp; t &lt; -2 \\
t+2 &amp;, \text{ for}  &amp;-2 &lt; t &lt; -1 \\
-t&amp;, \text{ for}  &amp; -1 &lt; t &lt; -0.5 \\
t+1 &amp;, \text{ for }   &amp;-0.5 &lt; t &lt; 0 \\
-2t+1 &amp;, \text{ for}  &amp; 0 &lt; t &lt; 0.5 \\
0 &amp;, \text{ for }   &amp;0.5 &lt; t \\
\end{cases}
$$ 

Expressing this using unit steps (alone) is not possible, you need the ramp functions. Then you can provide a representation using scaled and shifted ramps.

A MATLAB plot of the resulting signal is provided below ;