Final answer:
To solve the equation [(1/2)x-7]=[(1/3)(x-12)], we multiply by the common denominator, distribute, combine like terms, and isolate x to find the solution. The final solution is x = -3, and it's good practice to check by plugging it back into the original equation.
Step-by-step explanation:
To solve the equation given by [(⅓)x-7]=[(⅓)(x-12)], we need to first perform some algebraic manipulations. We will start by getting rid of the fractions to make the equation easier to work with. We do this by finding a common denominator, which is in this case 6 (since 2 and 3 are both divisors of 6), and then multiplying both sides of the equation by this common denominator.
Afterwards, we distribute the 6 to the terms on both sides, which will give us 3(x-7) = 2(x-12). Simplifying further, we expand the brackets to get 3x - 21 = 2x - 24. Next, we isolate the variable x by moving terms with x to one side and numeric terms to the opposite side, resulting in 3x - 2x = -24 + 21.
Combining like terms, we get x = -3. So, the solution to the equation is x = -3. With complex equations, it's always a good practice to plug back the solution into the original equation to ensure it's correct. Thus, checking the answer for reasonableness concludes the process.