Final answer:
The equation (2/3)=(x+9)/12 is solved by first multiplying both sides by 12 to eliminate the denominator, then simplifying and isolating x to find that x equals -1.
Step-by-step explanation:
To solve the equation (2)/(3)=(x+9)/(12), we first need to perform algebraic rearrangement. This involves finding a way to isolate the variable x on one side of the equation. To start, we can multiply both sides of the equation by 12 to eliminate the denominator on the right side:
12 * (2/3) = 12 * (x + 9) / 12
This simplification results in:
8 = x + 9
Next, we subtract 9 from both sides to isolate x:
8 - 9 = x + 9 - 9
Finally, we arrive at the solution:
-1 = x
Therefore, the value of x that satisfies the equation is -1.