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Question 88089: how can I Solve and graph the solution please help
7(x - 3) ˃5x -14
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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7(x-3) > 5x - 14
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Except for a rule, you can work with inequalities just as you would work with equations.
The exception is that if you multiply or divide both sides of an inequality by a negative
quantity then you must reverse the direction of the inequality sign. In this problem
you do not need to use this rule.
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Let's begin by doing the distributed multiplication on the left side of the inequality.
This multiplication results in:
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7x - 21 > 5x - 14
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Just as you would do if this were an equation, you collect all the terms involving
the variable x on one side and all the terms that are just numbers on the other side.
Begin by getting rid of the 5x on the right side by subtracting 5x from both sides of
the inequality. When you subtract 5x from both sides, the result is:
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2x - 21 > -14
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Next, get rid of the -21 on the left side. Do this by adding +21 to both sides. When you
do this addition you get:
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2x > +7
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Finally, solve for x by dividing both sides by +2. When you do this division, the result
is:
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x > 7/2
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You can graph this on the number line. On the number line put a dot at +7/2 which is
to say put a dot at 3.5 or 3 1/2.
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Then on the number line x can be any number that is greater than +7/2, that is to say
that x is any number that lies to the right of the point +7/2 on the number line. On
this graph you can make the number line to the right of +7/2 a heavier, broader line to
indicate that x can be any value on the heavier line. One of the ways that you can indicate
that on the graph that +7/2 is not in the solution set is to use a "(" symbol immediately to
the right of +7/2. This will show that as you move from right to left the heavier
line ends just before the point +7/2.
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Just to build our confidence that we have the correct answer, let' select a couple
of values for x and try them in the original equation. Let's first let x be +3. According
to our answer, that value of x is smaller than +7/2 so it should not work in the inequality.
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The original inequality is:
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7(x - 3) > 5x - 14
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Substitute +3 for x and you get:
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7(3 - 3) > 5(3) - 14
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7(0) > 15 - 14
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0 > 1
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But zero is not greater than 1. So when x = +3 the inequality does not work, and we had
said it should not.
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Now let's try letting x = +4 which is slightly bigger than +7/2. Substitute +4 for x
in the original inequality:
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7(x - 3) > 5x - 14
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7(4 - 3) > 5(4) - 14
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7(1) > 20 - 14
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7 > 6
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This is true! 7 is greater than 6 and so when x is +4 the inequality does work.
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This helps to confirm that +7/2 is the critical point on the number line where the value
of x changes one from that will not satisfy the inequality to one that will.
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Hope this helps you to understand the problem and how to find the range of variables
that will satisfy inequalities.
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