Solution sets must be given in interval and graph forms..

-4(z-5)> 2z-4 -4z+20> 2z-4 distributive property -4z> 2z-24 add 20 to each side -6z>-24 subtract 2z from both sides Z
by

-4(z-5) > 2z-4   Multiply both sides by -1, changing the orientation of the inequality sign.   We have:

4(z-5) < -2z+4  Rmove the brackets.   We have:

4z-20 < -2z+4   Add 2z+20 to both sides.   We have:

6z < 24   Divide both side by 6 to get z by itself.   We have: z < 4

The set of solutions are:

1. in interval notation: The set of solutions is: the interval (-∞, 4)

2. in graph:

1). Draw a number line of z.   A horizontal'd be convenient in many ways.

2). Mark a point z=0 on the line with a short vertical cut.   The far right of the line directs toward positive infinity.

3). Mark a point z=4 to the right of point 0, with a small empty babble/open circle.

4). Color the line from the babble to the left, or make the line a little thicker than the original.

The colored left defines the set of solutions, but the point of babble, z=4, is excluded.

by
edited