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Which value for x makes the open sentence true?

7 + 6x = 42 + x^2

A. 5.
B. 3.
C. 2.

1 Answer

4 votes

Final answer:

To find the value of x that makes the equation 7 + 6x = 42 + x^2 true, one must factor the quadratic equation x^2 - 6x + 35 = 0, yielding the solutions x = 5 and x = 7. With only x = 5 provided as an option, the correct answer is A. 5.

Step-by-step explanation:

The student asked which value for x makes the open sentence true: 7 + 6x = 42 + x2. To solve this, we need to rearrange the equation into the standard quadratic form ax2 + bx + c = 0. Subtracting 7 and 6x from both sides, we get:

x2 - 6x + (42 - 7) = 0
x2 - 6x + 35 = 0

Factoring the quadratic, we find:

(x - 5)(x - 7) = 0

Therefore, the possible values for x are 5 and 7. However, since 5 and 3 are the only options provided, and 5 is one of the factors, the correct answer is: A. 5.

Always remember to eliminate terms wherever possible to simplify the algebra, and after finding a solution, check the answer to see if it is reasonable (Practice Test 4, Solution 8.12).

User Ben Pingilley
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