Solve for X: 6.8 + (1/5 + 2/10)x = (3/5)x - 2.2 Equation

We have the equation:

$6.8 + \frac{1}{5}x + \frac{2}{10}x = \frac{3}{5}x - 2.2$

To solve this equation, let's follow these steps:

• Step 1: Convert all decimals to fractions for consistency and ease of calculation.
• Step 2: Combine like terms on both sides of the equation.
• Step 3: Rearrange the equation to isolate $x$.
• Step 4: Solve for $x$.

Now, let's work through each step:

Step 1: Convert decimals to fractions:
$6.8$ can be written as $\frac{68}{10} = \frac{34}{5}$ and
$2.2$ can be written as $\frac{22}{10} = \frac{11}{5}$.

Thus, the equation becomes:

$\frac{34}{5} + \frac{1}{5}x + \frac{2}{10}x = \frac{3}{5}x - \frac{11}{5}$

Step 2: Simplify the terms involving $x$:

$\frac{2}{10}$ simplifies to $\frac{1}{5}$, so the left side becomes:

$\frac{34}{5} + \frac{1}{5}x + \frac{1}{5}x = \frac{34}{5} + \frac{2}{5}x$

Step 3: Move all terms involving $x$ to one side and constants to the other side:

Subtract $\frac{2}{5}x$ from both sides:

$\frac{34}{5} = \frac{3}{5}x - \frac{2}{5}x - \frac{11}{5}$

Combine terms:

$\frac{34}{5} = \frac{1}{5}x - \frac{11}{5}$

Step 4: Solve for $x$ by eliminating constants from the right side:

Add $\frac{11}{5}$ to both sides:

$\frac{34}{5} + \frac{11}{5} = \frac{1}{5}x$

Combine the constants on the left:

$\frac{45}{5} = \frac{1}{5}x$

Since $\frac{45}{5} = 9$, it follows:

$9 = \frac{1}{5}x$

Finally, multiply both sides by 5 to isolate $x$:

$x = 9 \times 5$

$x = 45$

Therefore, the solution to the equation is $x = 45$.