The graph of the inequality is the shaded region and boundary of the inequality is . To graph the boundary, find the x-intercept and y-intercept of the line.

The inequality is 

The inequality is in slope-intercept form.

Apply subtraction property of equality: If a = b than a – c = b – c.

          (Subtract 0.5x from each side)

                       (Apply Additive inverse property: )

                             (Apply Additive identity property: )

To graph the inequality, first graph the

First find the y-intercept.

The y-intercept is the value of y, when .

                             (Substitute )

                                      (Apply zero product property: )

                                            (Apply Additive identity property: )

The y-intercept is 4, so the graph intersects the y-axis at (0, 4).

Next find the x-intercept.

The x-intercept is the value of x, when .

                           (Substitute )

               (Subtract 4 from each side)

Apply commutative property of addition: .

                          (Apply Additive inverse property: )

Apply division property of equality: If a = b than .

                         (Divide each side by 0.5)

                                 (Cancel common terms)

                                    (Divide: )

                     (Multiply each side by negative one)

                                          (Product of two same signs is positive)

The x-intercept is 8, so the graph intersects the x-axis at (8, 0).

To draw inequality follow the steps.

1.   Draw a coordinate plane.

2.  Plot the points.

3.  Since inequality symbol is <, the boundary is not included in the solution set. Graph the boundary of the inequality with a dashed line.

4.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute and y = 0 in original inequality .

The statement is true.

4.  Since the statement is true, shade the region that contains point (0, 0).

Inequality graph is