3) y> 4x -3 y2- 2x +3 ...

Given that,

$$\begin{gathered} y>4x-3 \\ y\ge -2x+3 \end{gathered}$$

Write the given inequality in equation form,

$$\begin{gathered} y=4x-3 ...\left(1\right) \\ y=-2x+3 ...\left(2\right) \end{gathered}$$

Equation (1),

When x = 0, y=-3,

When y = 0, $x=\frac{3}{4}=0.75$

Equation (1) passes through (0, -3) and (0.75, 0).

Equation (2),

When x = 0, y = 3

When y = 0, $x=\frac{3}{2}=1.5$

Equation (2) passes through (0, 3) and (1.5, 0).

Subtracting (1) from (2),

$$\begin{gathered} y-y=-2x+3-4x+3 \\ -6x+6=0 \\ 6x=6 \\ x=1 \end{gathered}$$

Substitute x = 1 in (1),

$y=4-3=1$

So intersection point of (1) and (2) is (1, 1).

Now take three points (1, 6), (0, 4) and (2, 7).

Substitute these three points in given inequality,

At (1, 6),

$$\begin{gathered} 6>4-3\Rightarrow 6>1 \\ 6\ge -2+3\Rightarrow 6\ge 1 \end{gathered}$$

At (0, 4),

$$\begin{gathered} 4>0-3\Rightarrow 4>-3 \\ 4\ge 0+3\Rightarrow 4\ge 3 \end{gathered}$$

At (2, 7),

$$\begin{gathered} 7>8-3\Rightarrow 7>5 \\ 7\ge -4+3\Rightarrow 7\ge -1 \end{gathered}$$

Hence these three points (1, 6), (0, 4) and (2, 7) satisfy the given inequality.

Graph:

[Shaded region represents the solution set of given equality included (1, 6), (0, 4) and (2, 7)]