Final answer:
The solution to the equation 6(x + 5) + 2 = 8(2x - 5) + 22 is x = 5, after distributing, combining like terms, and isolating the variable x.
Step-by-step explanation:
The solution for the equation 6(x + 5) + 2 = 8(2x - 5) + 22 is found by simplifying and solving for x. First, distribute the 6 and the 8 into the parentheses:
6x + 30 + 2 = 16x - 40 + 22.
Next, simplify both sides:
6x + 32 = 16x - 18.
Then, get all the x terms on one side and the constants on the other:
6x - 16x = -18 - 32.
This simplifies to:
-10x = -50.
Finally, divide by -10 to solve for x:
x = 5.
Therefore, the solution for the equation is x = 5, which corresponds to option B.