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

  • Thread starter Gringo123
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In summary, the conversation is about solving a given equation by multiplying both sides by a common denominator. However, the person making the attempt makes a mistake by incorrectly distributing a minus 1 over the second term in brackets. This results in a conclusion that is always false and therefore, incorrect. Another person in the conversation points out the mistake and explains that the correct solution for the equation is x = -4.
  • #1
Gringo123
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Can someone please tell me where I have gone wrong here? I have to solve the following equation:

(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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  • #2
You have incorrectly distributed the minus 1 over the second term in brackets.
 
  • #3
Hi Cyosis. Thanks for your reply. I'm afraid I don't understand. can you clarify your statement please?
Many thanks
 
  • #4
Sure, [tex]-(4x+5)=-4x-5 \neq \underbrace{-4x+5}_\text{what you did}[/tex].
 
  • #5
Gringo123 said:
...
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
Gringo123 said:
Can someone please tell me where I have gone wrong here? I have to solve the following equation:

(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
Susanne217 said:
[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
Borek said:
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...
 

Related to Solve Equation: 3x - 7/4 - (4x + 5)/2 = 3/4

1. How do I solve this equation?

To solve this equation, we need to first combine like terms on the left side. This means adding the coefficients of 3x and 4x, and the constants of -7/4 and 5. This results in -x - 7/4. On the right side, we have 3/4. To isolate x, we need to get rid of the -7/4, so we can add it to both sides. This results in -x = 3/4 + 7/4 = 10/4. Finally, we divide both sides by -1 to get x = -10/4 or x = -5/2.

2. What is the first step in solving this equation?

The first step in solving this equation is to combine like terms on the left side. This means adding the coefficients of 3x and 4x, and the constants of -7/4 and 5. This results in -x - 7/4.

3. How do I get rid of the fractions in this equation?

To get rid of the fractions in this equation, we can multiply both sides by the lowest common denominator (LCD) of all the fractions involved. In this case, the LCD is 4. Multiplying both sides by 4 will result in a new equation with no fractions.

4. What is the final solution to this equation?

The final solution to this equation is x = -5/2 or -2.5. This can be verified by substituting -5/2 into the original equation and simplifying, which will result in both sides being equal to 3/4.

5. Can this equation be solved using a calculator?

Yes, this equation can be solved using a calculator by entering the left side of the equation as an expression and the right side as a value, and then solving for x. However, it is important to note that understanding the steps and concepts involved in solving equations is crucial for a deeper understanding of mathematics and science.

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