Final answer:
The equation 'Four times the sum of some number and 2 is equal to 7 times the number minus 10' is solved by setting the unknown as x, forming the equation, rearranging it, and solving for x to get the answer, which is 6 (option C).
Step-by-step explanation:
To solve for the unknown number in the equation 'Four times the sum of some number and 2 is equal to 7 times the number minus 10,' first, we set up the equation. Let the unknown number be represented by x. The equation then is:
4(x + 2) = 7x - 10
Expanding the left side of the equation gives:
4x + 8 = 7x - 10
Then we move all terms involving x to one side and the constant terms to the opposite side to isolate the variable x:
4x - 7x = -10 - 8
-3x = -18
We then divide both sides by -3 to find the value of x:
x = (-18) / (-3)
x = 6
Therefore, the solution to the equation is x = 6, which is option C.