Step-by-step Answer
PAGE: 110SET: ExercisesPROBLEM: 46
Please look in your text book for this problem Statement

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.

First find the y-intercept.

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

                                          (Substitute )

                                                (Multiply: )

                                                  (Apply Additive identity property: )

The y-intercept is 5, so the graph intersects the y-axis at (0, 5).

Next find the x-intercept.

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

                                             (Substitute )

                               (Add 5 to each side)


                                             (Divide each side by 3)

                                                 (Cancel common terms)

                                               (Divide: )

The x-intercept is 1.66, so the graph intersects the x-axis at (1.66, 0).

To draw inequality follow the steps.

1.   Draw a coordinate plane.

2.  Plot the points.

3.  Since inequality symbol is , the boundary is included in the solution set. Graph the boundary of the inequality with a solid 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 false.

4.  Since the statement is false, shade the region that do not contains point (0, 0).

Linear inequality y less than or equal to 3x-5 graph

Inequality graph is

Linear inequality y less than or equal to 3x-5 graph


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