Question

Question #c7ff5

Answer 1

`x - 6 > 2x`

Explanation:

Let `x` represent the number.

1) Find the way to express the given values in terms of `x`

The number . . . . . . . . . . . . . . . `x`
6 less than the number . . . . . `x - 6`
Two times the number . . . . .`2x`

2) Write the inequality

`x - 6 > 2x` `larr` answer

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The problem here is that this doesn't seem to make sense.

How can a number have 6 subtracted from it, and then end up even bigger than double the number?

Suppose the number is `10`

Subtract `6` from `10`

That gives you `4`, clearly not greater than "double `10`," which is `20`.

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So that is your clue that "the number" must be a negative number.

If "the number" turns out to be `- 10`, then subtracting `6` from that gives you `-16.`

And `-16` really is greater than "double `-10`," which is `- 20`

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Solving the actual inequality:
`x - 6 > 2x`

Subtract `x` from both sides to get all the `x` terms together.
`- 6 > x`

So the number `x` is `-6`

It is perfectly true that `-6` is really more than `(2)("-"6)`
`(2)("-"6)` is way down at `-12`.
It's much more negative than `-6`