Solve for X: 1.7 - 1/6x + 3/6x = 3.5 + 2/12x Linear Equation

To solve this problem, we will perform the following steps:

• Step 1: Combine like terms on each side of the equation.
• Step 2: Simplify the equation by performing arithmetic operations.
• Step 3: Isolate the variable $x$ by using inverse operations to solve the equation.

Now, let's work through each step:

We start with the original equation:
$1.7 - \frac{1}{6}x + \frac{3}{6}x = 3.5 + \frac{2}{12}x$

Step 1: Simplify both sides by combining like terms.
On the left side, combine the terms with $x$:
$\frac{3}{6}x - \frac{1}{6}x = \frac{2}{6}x = \frac{1}{3}x$ The equation becomes:
$1.7 + \frac{1}{3}x = 3.5 + \frac{2}{12}x$

Notice that $\frac{2}{12}x$ can be simplified to $\frac{1}{6}x$

The equation is now:
$1.7 + \frac{1}{3}x = 3.5 + \frac{1}{6}x$

Step 2: To remove the fractions, find a common denominator for the coefficients of $x$, which is 6. Convert $\frac{1}{3}x$ to a fraction with 6 as the denominator:
$\frac{1}{3}x = \frac{2}{6}x$ Substitute in the equation:
$1.7 + \frac{2}{6}x = 3.5 + \frac{1}{6}x$

Subtract $\frac{1}{6}x$ from both sides:
$1.7 + \frac{2}{6}x - \frac{1}{6}x = 3.5$ This simplifies to:
$1.7 + \frac{1}{6}x = 3.5$

Subtract 1.7 from both sides to isolate the term with $x$:
$\frac{1}{6}x = 3.5 - 1.7$ $\frac{1}{6}x = 1.8$

Step 3: Solve for $x$ by multiplying both sides by 6 to clear the fraction:
$x = 1.8 \times 6$ Calculate the multiplication:
$x = 10.8$

Thus, the solution to the problem is $x = 10.8$.