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Question 100118: Hello, I need you help with one problem. I just don't have a real example.
2x-1 > 6x - 5
-
Thank You,
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! This is very similar to a problem that was posted previously. You are given to solve:
.
2x-1 > 6x - 5
.
What this means you are asked to find the values for +x that will make 2x - 1 be greater
than 6x - 5
.
You can work these as if the ">" sign were an "=" with one exception. That means that the
rules for solving equations apply ... except that if you MULTIPLY or DIVIDE both sides of
the inequality by a negative quantity, you must also reverse the direction of the inequality
sign.
.
Let's work this problem like an equation:
.
2x - 1 > 6x - 5
.
Get rid of the 6x on the right side by subtracting 6x from both sides:
.
2x - 6x - 1 > 6x - 6x - 5
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Do the subtractions on both sides to get:
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-4x - 1 > -5
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Now as you would do with an equation, get rid of the -1 on the left side by adding +1
to both sides:
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-4x - 1 + 1 > -5 + 1
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On the left side the - 1 + 1 cancel each other. On the right side the - 5 + 1 combine
to result in -4. This makes the inequality:
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-4x > -4
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But the problem requires us to solve for +x. So, just as you would do in an equation
let's solve for +x by dividing both sides by -4 because that is the multiplier of x.
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-4x/-4 > -4/-4
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The division results in:
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x > 1
.
But don't forget the rule about the direction of the inequality sign. When you divide
or multiply both sides by a minus quantity, you must also reverse the direction of the
inequality sign. We divided both sides by the minus quantity -4. Therefore, our answer must
have the inequality going in the opposite direction from what it was just before we did the
division by -4. Therefore, our answer is:
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x < 1
.
This means that for any value of x that is less than +1, the value of 2x - 1 will be
greater than the value of 6x - 5
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Let's set x = to zero, just to do a "confidence" check. Since 0 is less than 1, the value
we have chosen for x, we should find that 2x - 1 is greater than 6x - 5.
.
When x is 0, then 2x - 1 equals -1 and 6x - 5 is 6(0) - 5 = 0 - 5 = -5. This makes the original
inequality you were given as the problem become:
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-1 > -5
.
That is true. -1 is greater than -5 because -1 lies to the right of -5 on a number line.
Therefore, since this is true it helps to build your confidence that whenever x is less than
1, the given inequality will be true.
.
Hope this also helps you to see how to do these problems.
.
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