Solve for X: 6(x+4)-4 = 8(x+5) Linear Equation Solution

To solve this problem, we'll follow these steps:

• Expand both sides using the distributive property.
• Combine like terms and simplify.
• Isolate the variable $x$.

Let's work through the steps in detail:

Step 1: Apply the distributive property:
- Left side: $6(x+4)$ expands to $6x + 24$.
- Right side: $8(x+5)$ expands to $8x + 40$.
Substituting back, the equation becomes:

$6x + 24 - 4 = 8x + 40$

Step 2: Simplify the equation by combining like terms:
- 24 - 4 simplifies to 20 on the left-hand side.
The equation now is:

$6x + 20 = 8x + 40$

Step 3: Isolate the variable $x$:
- First, eliminate $6x$ from the left side by subtracting $6x$ from both sides:

$20 = 2x + 40$

- Next, eliminate 40 from the right side by subtracting 40 from both sides:

$20 - 40 = 2x$
$-20 = 2x$

Step 4: Solve for $x$ by dividing both sides by 2:

$x = \frac{-20}{2}$
$x = -10$

Therefore, the solution to the problem is $x = -10$.