Solve for X: 5(x-4)-6(7-x)=5x Linear Equation Solution

To solve the equation $5(x-4) - 6(7-x) = 5x$, we will simplify both sides and solve for $x$ step-by-step:

Step 1: Distribute Constants inside Parentheses
Apply the distributive property to simplify each group:
- $5(x-4)$ becomes $5x - 20$.
- $-6(7-x)$ becomes $-42 + 6x$.

Resulting Equation:
$5x - 20 - 42 + 6x = 5x$.

Step 2: Combine Like Terms
Combine $5x$ and $6x$, and $-20$ and $-42$:
- $5x + 6x = 11x$.
- $-20 - 42 = -62$.
The equation is now: $11x - 62 = 5x$.

Step 3: Isolate the Variable $x$
Subtract $5x$ from both sides to get the $x$-terms on one side:
$11x - 5x = 62$.
This simplifies to $6x - 62 = 0$.

Step 4: Solve for $x$
Add 62 to both sides to isolate the term with $x$:
$6x = 62$.
Now, divide by 6 to solve for $x$:
$x = \frac{62}{6} = \frac{31}{3} \approx 10.33$.

Therefore, $x \approx 10.33$.