Write down the three inequalities which define the shaded region on the axes below.

First, using your knowledge of Straight Line Graphs (y = mx + c), define the three lines as equations, ignoring inequality signs;

Now decide which inequality signs to use

For $y=x$, the shaded region is above the line, and the line is dotted, so the inequality is

$\mathit{y}\mathbf{>}\mathit{x}$

Check by substituting a point within the shaded region into this inequality. For example, using (2, 4) as marked on the graph above;

"$4>2$" is true, so the inequality $y>x$ is correct

For $y=-x+7$, the shaded region is below the line, and the line is solid, so the inequality is 

$\mathit{y}\mathbf{\le }\mathbf{-}\mathit{x}\mathbf{+}\mathbf{7}$
or $\mathit{y}\mathbf{+}\mathit{x}\mathbf{\le }\mathbf{7}$

Again, check by substituting (2, 4) into the inequality;

"$4\le -2+7$" is true, so the inequality $y\le -x+7$ is correct

For $x=1$, the shaded region is to the right of the solid line so the inequality is

$\mathit{x}\mathbf{\ge }\mathbf{1}$

(Vertical and horizontal inequality lines probably do not need checking with a point, though do so if you are unsure)