%3D9x-12-left(x-1-right)%24.jpeg "$ Frac 1 2 Left(4x+5 Right)=9x-12 Left(x-1 Right)$")
Solving the Equation: A Step-by-Step Guide
In this article, we will solve the equation $\frac{1}{2}(4x+5)=9x-12(x-1)$ using the principles of algebra.
Step 1: Simplify the Equation
First, let's simplify the equation by multiplying both sides by 2 to eliminate the fraction:
$2\left(\frac{1}{2}(4x+5)\right)=2(9x-12(x-1))$
This gives us:
$4x+5=18x-12x+12$
Step 2: Combine Like Terms
Next, let's combine like terms:
$4x+5=6x+12$
Step 3: Isolate the Variable
Now, let's isolate the variable $x$ by subtracting $5$ from both sides:
$4x=6x+7$
Subtracting $6x$ from both sides gives us:
$-2x=7$
Dividing both sides by $-2$ gives us the solution:
$x=\frac{-7}{2}$
Conclusion
Therefore, the solution to the equation $\frac{1}{2}(4x+5)=9x-12(x-1)$ is $x=\frac{-7}{2}$.
