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Question 74812This question is from textbook Algebra I
:
solve the inequality
5x<10(3x+4)
This question is from textbook Algebra I
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 5x<10(3x+4)
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You can treat problems such as this just like you would go about solving an equation ...
with one big exception. Any time that you multiply or divide both sides of the inequality
by a NEGATIVE quantity, you have to reverse the direction of the inequality arrow.
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Let's do your problem. Probably the first thing you see is that you have a multiplication
on the right side. Multiply it out to get:
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5x < 30x + 40
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Get all the terms containing x on one side of the inequality. Do this by subtracting
5x from both sides. When you do the inequality becomes:
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0 < 25x + 40
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Now get the number on the other side of the inequality. Do that by subtracting 40 from
both sides to get:
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-40 < 25x
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Finally, we are trying to solve for +x so divide both sides of the equation by +25, the
multiplier of x. When you do that you get:
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-40/25 < x
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And 25 goes into -40 ... -1.6 times. So the solution is:
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-1.6 < x
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You can read this as x must be greater than -1.6, and you can also write this as:
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x > -1.6
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And you could also write the -1.6 as -8/5 so you could write the solution as x > -8/5.
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Notice that we did not need to use the property that if you multiply or divide both sides
by a negative number, you reverse the direction of the inequality sign.
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Hope this allows you to do a few more inequality problems. Remember that as far as math
operations are concerned, you can use the same methods as you would to solve an equation.
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