How+is+solving+an+and+statement+different+from+solving+an+or+statement? +What+do+you+look+for+in+the+number+line+graphs?+Set+3

When you solve for an AND statement, you are looking for the set of numbers that satisfies __both__ equations or conditions given. Conversely, when you solve for an OR statement you are looking for the set of numbers that __either__ of the equations or conditions satisfy. The difference between these two statements is often made clearer when graphed on a number line.

The first two problems given below are and statements. The second two are or statements. How do the number line graphs of each look different? Notice how the and statement number line graph only shows the numbers that satisfy both equations, and the or statement number line graph shows the numbers that satisfy either equation. Also notice how only one of the and statements is a typical betweenness and only one of the or statements is a typical "outer" graph.

AND: 1) 5-2x>7 and 2x+7>1 2) 5x+2__<__12 and 10-2x>10

OR: 1) x+12>14 or 5x+2<-13 2) 2x+2>8 or 3x+1>16

__**Answer**__ AND: 1) -2x>2 --> **x<-1...** and... 2x>-6 --> **x>3** In this number line, the requirements have to apply to both inequalities. Therefore, a graph of these requirements would not be possible because a number cannot simultaneously be less than -1 while still being greater than 3. 2)5x__<__10 --> **x__<__2**... and... -2x>0 --> **x<0** This graph would be directional to the left. Because it is an "and" statement, the shaded area would begin after 0. In order to satisfy all the requirements of the inequality, the entire shaded region must be less than 0.

OR: 1) **x>2**... or... 5x<-15 --> **x<-3** This graph would have shaded arrows facing in two different directions. Because it is an or statement, this is necessary. Either of the requirements can be used at any given time, so the graph would be shaded to left of -3 and to the right of 2. 2) 2x>6 --> **x>3**... or... 3x>15 --> **x>5** This graph would only be shaded in one direction, but for a different reason than the "and" statement. In this graph, because only one of the restraints needs to be considered, the shaded region would begin at 3 and continue to the right.

-Erica