SOLUTION: Hello, I need you help with one problem. I just don't have a real example. 2x > 6x - 5

SOLUTION: Hello, I need you help with one problem. I just don't have a real example. 2x > 6x - 5 - Thank You,

Question 100117: Hello, I need you help with one problem. I just don't have a real example.
2x > 6x - 5
-
Thank You,
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are given to solve:
.
2x > 6x - 5
.
What this means you are asked to find the values for +x that will make 2x 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 > 6x - 5
.
Get rid of the 6x on the right side by subtracting 6x from both sides:
.
2x - 6x > 6x - 6x - 5
.
Do the subtractions on both sides to get:
.
-4x > -5
.
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.
.
-4x/-4 > -5/-4
.
The division results in:
.
x > 5/4
.
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:
.
x < 5/4
.
That means that for any value of x that is less than 5/4, the value of 2x will be greater
than the value of 6x - 5
.
Let's set x = to 1, just to do a "confidence" check. Since 1 is less than 5/4, the value
we have chosen for x, we should find that 2x is greater than 6x - 5.
.
When x is 1, then 2x equals 2 and 6x - 5 is 6(1) - 5 = 6 - 5 = 1. This makes the original
inequality you were given as the problem become:
.
2 > 1
.
That is certainly true, so it helps to build your confidence that whenever x is less than
5/4, the given inequality will be true.
.
Hope this helps you to see how to do these problems.
.
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