Algebra: identities & equations

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Algebraneophyte

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Hi guys.

I have attempted the following problem and am confused on whether there is an error in my book or not.......

Solve for c and d

-1(x+c) + 9(x+d) = 8x -53


My working:

1) Multiply out and collate terms:

8x - c + 9d = 8x -53

c = -1, d= -6

However my book lists c = 1 and d =6

Could you please help me tackle these :)
 
Algebraneophyte said:
Hi guys.

I have attempted the following problem and am confused on whether there is an error in my book or not.......

Solve for c and d

-1(x+c) + 9(x+d) = 8x -53


My working:

1) Multiply out and collate terms:

8x - c + 9d = 8x -53

c = -1, d= -6

However my book lists c = 1 and d =6

Could you please help me tackle these :)
Click to expand...
You are given one equation with multiple unknown s. You CANNOT solve for all the unknowns from there. You can derive the following relationship from there:

c - 9d = 53

From this you cannot derive unique values of c & d.

Please provide the COMPLETE & EXACT problem statement.
 
Hello. Thank you for replying.

The question is from an online question bank. The answer must factorize and expand into and from the brackets to first form an identity. Every time a different question is generated in all sections. I have attached a screenshot of this section.

Please help me understand how to answer for c and d:

Algebra Identity.png

Many Thanks.
 
Algebraneophyte said:
Hello. Thank you for replying.

The question is from an online question bank. The answer must factorize and expand into and from the brackets to first form an identity. Every time a different question is generated in all sections. I have attached a screenshot of this section.

Please help me understand how to answer for c and d:

View attachment 26816

Many Thanks.
Click to expand...
Aha. As Dr. Peterson said, there are an infinite number of pairs of numbers that meet the conditions specified. So if you interpret the question to mean find THE pair that meets the conditions, the question is impossible to solve. But the question does not use the definite article. What it means is to find A pair. The question could be better worded.

Learn to check your own work

[MATH](-1) - 9(-6) = 54 - 1 = 53 \ne - 53.[/MATH]
 
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