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# Simplify the expression \$(x-4)(x-7) + (3-x)(2+x).\$

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Hi, I need help with this problem, I tried every possible way and got 17/5 every time, I even checked Wolfram Alpha and it also says the answer is 17/5, Aops says this answer is wrong, plz show me what I did wrong with my calculations!

Jan 29, 2021

#1
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x^2 -11x+28      + 6 +3x-2x-x^2   = 0 (?)

-10x +34

10x = 34

x = 34/10 = 17/5

Jan 29, 2021
#2
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It says that's wrong.

Jan 29, 2021
#8
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That's why I added the  =0 (?)     But you didn't respond !

Guest Jan 29, 2021
#3
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Without doing any algebra, I can already tell that your answer of 17/5 cannot possibly be correct. This expression requires multiplication and addition of integers and variables, so it is impossible that the answer would yield a rational number.

Anyway, let's see what the real answer is, shall we?

\((x-4)(x-7) + (3-x)(2+x)\\ x^2-7x-4x+28+6+3x-2x-x^2\\ -10x+34\)

This is as far as we can simplify this expression. Remember that this expression is not an equation. I believe your mistake was that you set this expression equal to 0 and solved.

Jan 29, 2021
#4
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Oh, ok, thanks for the help.

Jan 29, 2021
#5
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Yes, you are welcome. Just remember not to convert an expression into an equation. This is a fairly common mistake. Good luck on your future algebraic adventures!

Guest Jan 29, 2021
#6
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(x – 4)(x – 7) + (3 – x)(2 + x)

(x2 – 11x + 28) + (–x2 + x +6)

x2 – x2 – 11x + x + 28 + 6

–10x + 34

simplified this is  2(17 – 5x)

Nothing in the problem you provided said to set the expression equal to zero and solve for x.

.

Jan 29, 2021
#7
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note for the future: on aops, "simplify" on equations with variables means "combine like terms then write out the equation in terms of the variable".

I use aops so trust me. I've done like 100 questions on simplifying expressions.

Jan 29, 2021
edited by KitSoundwave  Jan 29, 2021
edited by KitSoundwave  Jan 29, 2021
#9
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I use Aops too.

Feb 4, 2021
#10
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btw, I figured out the answer.

Feb 4, 2021