SOLUTION: Inequality solving: 28x+4<9

Question 511650: Inequality solving:
28x+4<9
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
As a general rule, you can work inequalities using the same rules as you would for equations with the following exceptions:
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(1) If you multiply both sides by a negative number, reverse the direction of the inequality sign.
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(2) If you divide both sides by a negative number, reverse the direction of the inequality sign.
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(3) If you invert both sides (that is, flip fractions upside down on both sides), reverse the direction of the inequality sign.
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Given those three exceptions, let's now work your problem using the same rules as you would for an equation. Your problem is:
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Subtract 4 from both sides to get the term containing the x by itself on the left side. After subtracting 4 from both sides you have:
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Now to solve for x, divide both sides by +28 and you have:
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And that's the answer. x must be smaller than .
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Note that in solving this problem, we did not need to apply any of the three exceptions listed above. Save those exceptions for another problem in which you may have to use them.
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Notice too that in working this problem we treated the < sign as if it were an = sign so that we could work the problem just as we would solve an ordinary equation. Then at the end, we ensured that the < sign was still used in the same direction as before because we did not need to change it due to using any of the exceptions listed above.
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Hopefully this explanation will help you to work other inequality problems also.

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