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Unformatted text preview: Inequality Signs Read left to right: a < b a is less than b a < b a is less than or equal to b a > b a is greater than b a > b a is greater than or equal to b Interval Notation Interval notation is a way to notate the range of values that would make an inequality true. There are two types of intervals, open and closed (described below), each with a specific way to notate it so we can tell the difference between the two. Note that in the interval notations (found below), you will see the symbol , which means infinity . ty ( ) means it goes on and on indefinitely to the right of the number  there is no endpoint on the right. Negative infinity ( ) means it goes on and on indefinitely to the left of the number  there is no endpoint to the left. Since we dont know what the largest or smallest numbers are, we need to use infinity or negative infinity to indicate there is no endpoint in one direction or the other. In general, when using interval notation, you always put the smaller value of the interval first (on the left side), put a comma between the two ends, then put the larger value of the interval (on the right side). You will either use a curved end ( or ) or a boxed end [ or ], depending on the type of interval (described below). If you have either infinity or negative infinity on either end, you always use a curve for that end. This will indicate that there is no definite endpoint in that direction, it keeps going and going. Open Interval An open interval does not include where your variable is equal to the endpoint. To indicate this, we use a curved end as shown below. Inequality Interval Notation for Open Intervals x > a ( a , ) x < a ( , a ) When you graph an open ended end point, you use the same curved end ( or ) on the graph as you do in the interval notation. Also, darken in the part of the graph that is the solution. For example, Inequality Interval Notation for Open Intervals Graph x > 4 (4, ) x < 4 ( , 4) Closed Interval A closed interval includes where your variable is equal to the endpoint. To indicate this, we use a boxed end as shown below. As mentioned above, even though a is included and has a boxed end, if it goes to either infinity or negative infinity on the other end, we will notate it with a curved end for that end only! Inequality Interval Notation for Closed Intervals x > a [ a , ) x < a ( , a ] When you graph a closed ended end point, you use the same boxed end [ or ] on the graph as you do in the interval notation. Also, darken in the part of the graph that is the solution. For example, Inequality Interval Notation for Closed Intervals Graph x > 4 [4, ) x < 4 ( , 4] Combining Open and Closed Intervals Sometimes one end of your interval is open and the other end is closed. You still follow the basic ideas described above. The closed end will have a [ or ] on its end and the open end will have a ( or ) on its end....
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 Spring '11
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 Algebra

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