Solve the Linear Equation: Break Down -2x + 4 + 10x - 8 = 3 - 4x + 17

To solve for $x$ in the given equation $-2x + 4 + 10x - 8 = 3 - 4x + 17$, follow these steps:

• Step 1: Simplify both sides of the equation.

Start with the left-hand side of the equation:

$-2x + 4 + 10x - 8$ simplifies to:

$(-2x + 10x) + (4 - 8) = 8x - 4$

Now, simplify the right-hand side:

$3 - 4x + 17$ combines to:

$(3 + 17) - 4x = 20 - 4x$

• Step 2: Rearrange the equation to place all variable terms on one side and constant terms on the other.

We have:

$8x - 4 = 20 - 4x$

Add $4x$ to both sides to collect all $x$-terms on the left:

$8x + 4x - 4 = 20$

This simplifies to:

$12x - 4 = 20$

• Step 3: Solve for $x$.

Add 4 to both sides to isolate the terms with $x$:

$12x = 24$

Finally, divide by 12 to solve for $x$:

$x = \frac{24}{12} = 2$

Therefore, the solution to the equation is $x = 2$.