Final answer:
The value of m that makes the equation 12x + 18 = 2(6x + m) – 6 true for any x is 12.
Step-by-step explanation:
To determine the value of m that makes the equation 12x + 18 = 2(6x + m) – 6 true for any x, we first expand the right side of the equation:
12x + 18 = 12x + 2m – 6.
Now we simplify and solve for m.
18 + 6 = 2m,
24 = 2m.
Finally, we divide by 2 to find m:
m = 12.
Thus, the value of m that satisfies the equation for any x is 12.