3a + 3b: Solving the Equation
In algebra, equations are used to solve for unknown variables. One type of equation is the linear equation, which can be written in the form of ax + by = c, where a, b, and c are constants, and x and y are variables. In this article, we will discuss the solution to the equation 3a + 3b.
What does 3a + 3b mean?
The equation 3a + 3b is a linear equation that combines two variables, a and b, with a coefficient of 3. The coefficient 3 means that the variables a and b are being multiplied by 3.
How to solve 3a + 3b?
To solve for 3a + 3b, we need to isolate one of the variables. Since we have two variables, we can use substitution or elimination methods. Let's use the elimination method.
Step 1: Write the equation
3a + 3b = ?
Step 2: Factor out the common term
3(a + b) = ?
Step 3: Divide by 3
a + b = ?
Solution
The solution to the equation 3a + 3b is a + b. This means that the sum of a and b is equal to the original equation.
Example
Let's say we have the equation 3a + 3b = 12. To solve for a and b, we can use the solution above:
a + b = 12
Now, we can substitute values for a and b to find the solution. For example:
a = 4, b = 8
or
a = 2, b = 10
Both solutions satisfy the equation 3a + 3b = 12.
Conclusion
In conclusion, the solution to the equation 3a + 3b is a + b. By factoring out the common term and dividing by 3, we can simplify the equation and solve for the variables. This equation is a basic example of a linear equation, and understanding how to solve it is essential for more complex algebraic equations.
