Solve for X: Combining Like Terms in 6.5x - 3.4x + 15 = 16 + 17 + 4.8x

Let's solve the equation step by step:

We start with the given equation:

$6.5x - 3.4x + 15 = 16 + 17 + 4.8x$

Step 1: Simplify the equation by combining like terms on each side.

• On the left-hand side, combine the $x$-terms: $6.5x - 3.4x = 3.1x$.
• So, the left-hand side becomes $3.1x + 15$.
• On the right-hand side, combine the constants: $16 + 17 = 33$.
• So, the right-hand side becomes $33 + 4.8x$.

We now have:

$3.1x + 15 = 33 + 4.8x$

Step 2: Move the terms involving $x$ to one side and the constant terms to the other side.

• Subtract $4.8x$ from both sides: $3.1x - 4.8x + 15 = 33$.
• Simplify to get: $-1.7x + 15 = 33$.
• Subtract 15 from both sides to move the constant: $-1.7x = 33 - 15$.
• That simplifies to: $-1.7x = 18$.

Step 3: Solve for $x$ by dividing both sides by $-1.7$.

$x = \frac{18}{-1.7}$

Calculating this gives:

$x \approx -10.58823529$

Rounding to two decimal places, we find:

$x \approx -10.58$

Therefore, the solution to the equation is $x = -10.58$.