Solving Inequalities | MathHelp.com - By MathHelp.com
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| 00:0-1 | When you're asked to solve an inequality like -3 , | |
| 00:04 | X is less than 12 . Your goal should be | |
| 00:08 | the same as it was when solving equations to get | |
| 00:11 | X by itself on one side In this problem , | |
| 00:16 | since X is being multiplied by -3 on the left | |
| 00:20 | side of the inequality to get X by itself , | |
| 00:24 | we divide both sides by negative three . Mhm . | |
| 00:32 | But here's the rule you have to watch out for | |
| 00:34 | when solving inequalities . When you divide both sides of | |
| 00:39 | an inequality by a negative number , you must switch | |
| 00:43 | the direction of the inequality sign . So this less | |
| 00:48 | than in our original problem becomes greater than in our | |
| 00:55 | second step on the left side , the negative threes | |
| 01:00 | cancel and we're left with X . And on the | |
| 01:05 | right side 12 divided by -3 is -4 . So | |
| 01:11 | we have X is greater than negative four . Our | |
| 01:17 | next task is to Graph X is greater than -4 | |
| 01:21 | on a number line . And to do that , | |
| 01:25 | we start with an open dot at negative four . | |
| 01:32 | The reason we use an open dot at negative four | |
| 01:35 | is that X is greater than -4 , but it | |
| 01:39 | is not equal to negative . For next we draw | |
| 01:43 | an arrow going to the right on our number line | |
| 01:49 | To represent all numbers greater than -4 . Finally , | |
| 01:56 | we put our answer in what is called set notation | |
| 02:01 | , which is written in the following way . The | |
| 02:04 | set of all X is such that X is greater | |
| 02:11 | than negative four and this is our final answer . | |
| 02:19 | All this means is that if we take any number | |
| 02:23 | greater than negative four and plug it back in for | |
| 02:27 | X in our original problem , we'll get a true | |
| 02:31 | statement , Try one . |
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