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).