Solve equation
7+3x-12x=3x+1
The Correct Answer and Explanation is :
To solve the equation ( 7 + 3x – 12x = 3x + 1 ), we first simplify both sides of the equation.
- Combine like terms on the left side:
[
7 + 3x – 12x = 7 – 9x
]
So the equation simplifies to:
[
7 – 9x = 3x + 1
] - Move all terms involving ( x ) to one side and constant terms to the other:
To isolate ( x ), we can add ( 9x ) to both sides:
[
7 = 3x + 9x + 1
]
Which simplifies to:
[
7 = 12x + 1
] - Subtract 1 from both sides:
[
7 – 1 = 12x
]
This gives us:
[
6 = 12x
] - Divide both sides by 12:
[
x = \frac{6}{12}
]
Simplifying this gives:
[
x = \frac{1}{2}
]
Explanation
The equation ( 7 + 3x – 12x = 3x + 1 ) contains terms involving the variable ( x ) and constant numbers. The goal is to isolate ( x ) on one side of the equation to find its value. We start by simplifying the left-hand side by combining the like terms, which allows us to rewrite the equation in a clearer form.
Next, we move all terms with ( x ) to one side of the equation and the constants to the other. This is done through simple arithmetic operations: adding or subtracting terms from both sides to maintain equality. By following these algebraic principles, we isolate the variable step-by-step, which leads us to a clear value for ( x ).
Finally, we simplify our result. The division step is crucial because it shows that ( x ) equals half, which is often a straightforward but vital part of solving algebraic equations. Thus, the solution to the original equation is ( x = \frac{1}{2} ).