- #1

- 141

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(3x - 7)/4 - (4x + 5)/2 = 3/4

I attempted to do it by muliplying boths sides by 4 to get rid of the denominators, leaving me with:

3x - 7 - 8x + 10 = 3

simplified: -5x + 3 = 3

which is clearly nonsense as that means -5x would equal 0.

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- Thread starter Gringo123
- Start date

- #1

- 141

- 0

(3x - 7)/4 - (4x + 5)/2 = 3/4

I attempted to do it by muliplying boths sides by 4 to get rid of the denominators, leaving me with:

3x - 7 - 8x + 10 = 3

simplified: -5x + 3 = 3

which is clearly nonsense as that means -5x would equal 0.

- #2

Cyosis

Homework Helper

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You have incorrectly distributed the minus 1 over the second term in brackets.

- #3

- 141

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Many thanks

- #4

Cyosis

Homework Helper

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Sure, [tex]-(4x+5)=-4x-5 \neq \underbrace{-4x+5}_\text{what you did}[/tex].

- #5

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...

simplified: -5x + 3 = 3

which is clearly nonsense as that means -5x would equal 0.

Besides what Cyosis said, there's another problem here...

If you reach the conclusion that -5x = 0 in an arbitrary equation, there is nothing (necessarily) wrong with that. Just divide both sides by -5 and the result is that x = 0. "-5x = 0" is false for many values of x, but it is not ALWAYS false, as we have seen.

If you reach a conclusion that is ALWAYS false (e.g. " 1=2 "), then that is nonsense.

x = 0 would have been the solution, had you arrived at -5x = 0 in a correct way.

- #6

- 317

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(3x - 7)/4 - (4x + 5)/2 = 3/4

I attempted to do it by muliplying boths sides by 4 to get rid of the denominators, leaving me with:

3x - 7 - 8x + 10 = 3

simplified: -5x + 3 = 3

which is clearly nonsense as that means -5x would equal 0.

If you put it on a commen dinominator

like this [tex]\frac{(3x-7)-(8x+10)}{4} = \frac{3}{4}[/tex] and multiply both sides by 4 and clean up the act you get

[tex]-5x -17 = 3 \Leftrightarrow -5x = 20 [/tex] and thus the only x which solves the original eqn is x = -4.

Last edited:

- #7

Borek

Mentor

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[tex]\frac{(3x-7)-(8x+10)}{4} = \frac{3}{4}[/tex] and multiply both sides by 4 and clean up the act you get

[tex]-5x + 3 = 3 \LeftRightarrow -5x = 0 [/tex]

No, you did exactly the same mistake Gringo did. -7-(+10) is not 3.

- #8

- 317

- 0

No, you did exactly the same mistake Gringo did. -7-(+10) is not 3.

Its gringa, jefe ;)

and sorry its early here in my part of the Univers...

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