Final answer:
The equation 12x + 6 = 14(2x - 24) has one solution, which is x = 21.
Step-by-step explanation:
To solve the equation, we need to distribute the 14 to both terms inside the parentheses: 12x + 6 = 14*2x - 14*24. This gives us 12x + 6 = 28x - 336.
Next, we need to isolate the x term by moving all the x terms to one side of the equation and the constant terms to the other side. Subtracting 12x from both sides gives us 6 = 16x - 336.
Finally, we can solve for x by adding 336 to both sides and then dividing by 16: x = (6 + 336)/16. After simplifying, we get x = 21.