Final answer:
The solution to the equation 3x + 2 = 5(x - 4) is found by distributing, combining like terms, and isolating the variable x, which results in x = 11. Therefore, the correct option is d. x ≥ 11.
Step-by-step explanation:
When solving the equation 3x + 2 = 5(x - 4), we first distribute the 5 on the right-hand side of the equation:
3x + 2 = 5x - 20
Next, we combine like terms by subtracting 3x from both sides:
2 = 2x - 20
We then add 20 to both sides to isolate the term with the variable x:
22 = 2x
Finally, we divide both sides by 2 to solve for x:
x = 11
Therefore, the solution to the equation is x = 11. Looking at the provided options, the correct answer is d. x ≥ 11. This indicates that x is greater than or equal to 11, which makes sense since we have found that x is precisely 11.