Solve 3(x-4)=12x pls
The Correct Answer and Explanation is:
Let’s solve the equation ( 3(x – 4) = 12x ).
Step 1: Distribute the 3 on the left side
First, use the distributive property to expand the left side of the equation:
[
3(x – 4) = 3 \cdot x – 3 \cdot 4 = 3x – 12
]
So, the equation becomes:
[
3x – 12 = 12x
]
Step 2: Get all terms with ( x ) on one side
Next, we want to get all the ( x )-terms on one side of the equation. To do this, subtract ( 3x ) from both sides of the equation:
[
3x – 12 – 3x = 12x – 3x
]
Simplifying both sides:
[
-12 = 9x
]
Step 3: Isolate ( x )
Now, to solve for ( x ), divide both sides of the equation by 9:
[
\frac{-12}{9} = \frac{9x}{9}
]
Simplifying:
[
x = \frac{-12}{9} = \frac{-4}{3}
]
So, the solution is:
[
x = \frac{-4}{3}
]
Explanation:
In this problem, we used basic algebraic principles to isolate ( x ). The distributive property allowed us to expand the expression on the left side of the equation. Then, by combining like terms and isolating the variable, we moved all the ( x )-terms to one side and the constants to the other. Finally, we divided both sides by the coefficient of ( x ) to find its value.
This is a linear equation, meaning that the highest power of the variable is 1. Solving for ( x ) involves straightforward algebraic steps, such as distribution, combining like terms, and isolating the variable. The process demonstrates the fundamental method of solving for an unknown in an equation. In this case, the final solution is ( x = \frac{-4}{3} ), which is the value of ( x ) that satisfies the original equation.