#### Answer

See image
.

#### Work Step by Step

Apply
$\quad |x|=\left\{\begin{array}{ll}
x, & x\geq 0\\
-x, & x \lt 0
\end{array}\right.$
in each of the four quadrants.
We obtain an inequality per quadrant
$\left[\begin{array}{l|l|ll}
& y\geq 0 & & y \lt 0\\
\hline& & & \\
x\geq 0 & x+y\leq 1 & & x-y\leq 1\\
& (Q.I) & & (Q.IV)\\
\hline& & & \\
x \lt 0 & -x+y\leq 1 & & -x-y\leq 1\\
& (Q.II) & & (Q.III)
\end{array}\right]$
In quadrant $I$,
$y\leq-x+1 \quad$ test point (0,0) satisfies the inequality.
Intercepts $(1,0)$ and $(0,1)$.
This is the region below the line $y=-x+1$
In quadrant $II$,
$y\leq x+1 \quad \quad$ test point (0,0) satisfies the inequality.
Intercepts $(-1,0)$ and $(0,1)$.
This is the region below the line $y=x+1$, a triangle.
In quadrant $III$,
$-x-1\leq y \quad \quad$ test point (0,0) satisfies the inequality.
Intercepts $(-1,0)$ and $(0,-1)$.
This is the region above the line $y=-x-1$, a triangle.
In quadrant $III$,
$x-1\leq y \quad \quad$ test point (0,0) satisfies the inequality.
Intercepts $(1,0)$ and $(0,-1)$.
This is the region above the line $y=x-1$, a triangle.
The solution region contains all the above triangles.
All the borders are included (graphed with a solid line), since the inequalities include the "$=$" sign.