Solve the Equation with Constants 74.1 and 18.8 to Find X

Let's solve the problem step-by-step:

• Step 1: Combine like terms on both sides of the equation.

The given equation is:

$74.1 - 3.5x + 10.2x = 13.2x - 16.7 - 18.8$

First, combine like terms on the left-hand side (LHS):

$-3.5x + 10.2x = 6.7x$
Thus, the LHS becomes $74.1 + 6.7x$.

Combine constant terms on the right-hand side (RHS):

$-16.7 - 18.8 = -35.5$

Thus, the RHS becomes $13.2x - 35.5$.

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

Rearrange the equation:

$74.1 + 6.7x = 13.2x - 35.5$

Let's bring all terms with $x$ to one side by subtracting $6.7x$ from both sides:

$74.1 = 13.2x - 6.7x - 35.5$

This simplifies to:

$74.1 = 6.5x - 35.5$

• Step 3: Solve for $x$.

Add $35.5$ to both sides to isolate terms with $x$:

$74.1 + 35.5 = 6.5x$

$109.6 = 6.5x$

Finally, divide both sides by $6.5$:

$x = \frac{109.6}{6.5}$

Calculate the division:

$x = 16.86$

Therefore, the solution to the problem is $x = 16.86$.