Solve the Linear Equation: Arrange to Find X in -5x + 3 - 8 + 4x = 3x - 5 + 10x

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

• Simplify both sides of the equation.
• Combine like terms to isolate $x$.
• Solve for $x$ by equating coefficients.

Now, let's work through each step:

Step 1: Simplify both sides
The original equation is:

$-5x + 3 - 8 + 4x = 3x - 5 + 10x$

Simplify each side by combining like terms:

Left side: $-5x + 4x + 3 - 8$ becomes $-x - 5$.

Right side: $3x + 10x - 5$ becomes $13x - 5$.

Now the equation is:

$-x - 5 = 13x - 5$

Step 2: Remove like terms
Add $x$ to both sides to move terms involving $x$ together:

$-5 = 14x - 5$

Step 3: Isolate the constant terms:
Add 5 to both sides:

$0 = 14x$

Step 4: Solve for $x$
Divide both sides by 14:

$x = 0$

Therefore, the solution to the problem is $x = 0$.