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| Math Central | Quandaries & Queries |
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Question from Deborah, a student: 2(v+10)<18 |
Hi Deborah,
I am going to solve a similar problem.
Solve for x if 2(4 - 3x) < 14.
You can solve this type of inequality just as you would solve an equality with one extra condition. If you multiply or divide both sides by a negative number you must reverse the direction of the inequality. Here's what I mean.
Solve for x if 2(4 - 3x) = 14.
Solution.
| 2(4 - 3x) = 14 | divide both sides by 2 |
| 4 - 3x = 7 | subtract 4 from each side |
| -3x = 3 | divide both sides by -3 |
| x = -1 |
Now the inequality.
Solve for x if 2(4 - 3x) < 14.
Solution.
| 2(4 - 3x) < 14 | divide both sides by 2 |
| 4 - 3x < 7 | subtract 4 from each side |
| -3x < 3 | divide both sides by -3 |
| x > -1 |
The steps are the same except that the equal sign is replaced by the less than sign and at the last step, since I divided by a negative number I reversed the less than sign and got a greater than sign.
Now try your problem,
Penny
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