Solving the Linear Equation: 3(x-4)=12x

Solving linear equations is a fundamental skill in high school mathematics. In this article, we will walk through the step-by-step process of solving the equation 3(x-4)=12x.

Step 1: Distribute the Coefficient

The first step in solving this equation is to distribute the coefficient 3 on the left-hand side of the equation:

3(x-4) = 12x 3x - 12 = 12x

Step 2: Combine Like Terms

Next, we need to combine the like terms on the left-hand side of the equation:

3x - 12 = 12x 3x - 12x = 0 -9x = -12

Step 3: Isolate the Variable

To isolate the variable x, we need to divide both sides of the equation by -9:

-9x = -12 x = -12/-9 x = 4/3 or x = 1.33

Therefore, the solution to the equation 3(x-4)=12x is x = 4/3 or x = 1.33.

It's important to note that when solving linear equations, there can be one, zero, or infinitely many solutions. In this case, the equation 3(x-4)=12x has a single solution.

I hope this step-by-step explanation helps you understand the process of solving linear equations. If you have any further questions or need additional practice, don't hesitate to reach out to your math teacher or explore more resources on solving linear equations.