-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.