Solve for X: 1/7x - 0.5 + 2/14x = 2/7x + 8.5

To solve the equation $\frac{1}{7}x - 0.5 + \frac{2}{14}x = \frac{2}{7}x + 8.5$, we need to proceed with the following steps:

• Step 1: Simplify the equation by combining like terms.

Examine the left-hand side (LHS):

$\frac{1}{7}x + \frac{2}{14}x - 0.5$

Firstly, note that $\frac{2}{14}$ simplifies to $\frac{1}{7}$. Therefore, the LHS becomes:

$\frac{1}{7}x + \frac{1}{7}x - 0.5$.

Combine like terms:

$\left(\frac{1}{7}x + \frac{1}{7}x\right) - 0.5 = \frac{2}{7}x - 0.5$.

• Step 2: Compare both sides of the equation.

The right-hand side (RHS) is:

$\frac{2}{7}x + 8.5$.

Substitute the simplified LHS and RHS:

$\frac{2}{7}x - 0.5 = \frac{2}{7}x + 8.5$.

• Step 3: Analyze the equation for a solution.

Subtract $\frac{2}{7}x$ from both sides:

$-0.5 = 8.5$.

This results in a contradiction, since $-0.5$ does not equal $8.5$.

• Conclusion:

The equation does not have a solution. The coefficients of $x$ cancel each other out, and the remaining statement is false, indicating that no value of $x$ can satisfy the equation.

Therefore, the correct answer is: "No solution".