Solve for X: Simplifying 54x - 36x + 34 = 39 + 5x - 18

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

• Step 1: Simplify both sides of the given equation.
• Step 2: Isolate the variable $x$ on one side of the equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Simplify both sides of the equation.

The original equation is $54x - 36x + 34 = 39 + 5x - 18$.

On the left side, combine like terms: $54x - 36x = 18x$.

So, the equation becomes $18x + 34 = 39 + 5x - 18$.

Simplify the right side: $39 - 18 = 21$.

This gives us $18x + 34 = 21 + 5x$.

Step 2: Isolate the variable $x$ on one side.

Subtract $5x$ from both sides to get all $x$ terms on one side:

$18x - 5x + 34 = 21$.

This simplifies to $13x + 34 = 21$.

Subtract 34 from both sides to move constant terms to the other side:

$13x = 21 - 34$.

This simplifies to $13x = -13$.

Step 3: Solve for $x$.

Divide both sides by 13 to solve for $x$:

$x = \frac{-13}{13}$.

This simplifies to $x = -1$.

Therefore, the solution to the problem is $x = -1$.