Find X: Solving the Linear Equation 5 - 3x = 8x - 17

To solve this linear equation, follow these steps:

• Step 1: Move all terms involving $x$ to one side of the equation.
• Step 2: Move constant terms to the opposite side.
• Step 3: Simplify the equation to isolate $x$.
• Step 4: Solve for $x$ by dividing by its coefficient.

Let's work through it:

Start with the given equation:
$5 - 3x = 8x - 17$

Step 1: Add $3x$ to both sides to move all $x$ terms to the right side:
$5 = 11x - 17$

Step 2: Add $17$ to both sides to move the constants to the left side:
$22 = 11x$

Step 3 & 4: Divide both sides by $11$ to isolate $x$:
$x = \frac{22}{11}$

Simplifying the fraction gives:
$x = 2$

Hence, the solution to the problem is $x = 2$.