Solve for X: 6.8 - 15x + 7x = 3.4 - 5.1 + 8x Linear Equation

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

• Step 1: Simplify both sides of the equation
• Step 2: Move all $x$ terms to one side and constants to the other side
• Step 3: Solve for $x$

Now, let's work through each step:
Step 1: Simplify both sides of the equation:

On the left side, combine like terms:
$6.8 - 15x + 7x = 6.8 - 8x$

On the right side, simplify:
$3.4 - 5.1 + 8x = -1.7 + 8x$

This gives us the simplified equation:
$6.8 - 8x = -1.7 + 8x$

Step 2: Move all $x$ terms to one side and constants to the other side.

Add $8x$ to both sides to move $x$ terms to one side:
$6.8 - 8x + 8x = -1.7 + 8x + 8x$
This simplifies to:
$6.8 = -1.7 + 16x$

Subsequently, add $1.7$ to both sides to move constants to the opposite side:
$6.8 + 1.7 = 16x$

This simplifies to:
$8.5 = 16x$

Step 3: Solve for $x$.

Divide both sides by 16 to isolate $x$:
$\frac{8.5}{16} = x$

This simplifies to:
$x = 0.53125$

Rounding to two decimal places yields:
$x = 0.53$

Therefore, the solution to the problem is $x = 0.53$.