SOLUTION: I need to solve the following inequalities and show on the real number line. 3(2-3x)>5[x-2(x+5)]

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Question 70626: I need to solve the following inequalities and show on the real number line.
3(2-3x)>5[x-2(x+5)]
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!

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Start by treating this just as you would an equation and solve for x. First multiply out
the left side. When you do the result is:
.

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Next on the right side multiply out the -2 times (x+5). When you do the inequality
becomes:
.

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Then on the right side combine the x and -2x to get just -x. The inequality is then:
.

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Finally multiply out the right side:
.

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To cancel out the +6 on the left side, add a negative 6 to both sides. The inequality is
then"
.

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And to cancel out the -5x on the right side, add +5x to both sides. The result is:
.

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To solve this for positive x, divide both sides by -4. But now you have to remember the
rule ... whenever you divide or multiply both sides of an inequality by a negative number,
the inequality reverses direction. Dividing by -4 and reversing the inequality gives you:
.

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This tells you that when x is less than 14 the inequality of the original problem is
satisfied. And when x is 14 or more, the inequality of the original problem will not work.
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Try a few values of x less than 14 and see if they don't work. Try x=14 and see why it doesn't
work. And try a value or two for x greater than 14 to verify that they don't work.
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Note 0 is less that 14, so you can try it. It makes all the x's disappear and the problem
is simplified because of that.
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Hope this helps you understand inequalities a little better. And don't forget the rule
about multiplying or dividing inequalities by a negative number.