Solve for X: Finding the Solution to 4/5x + 3/7 = 2/14

To solve the linear equation $\frac{4}{5}x + \frac{3}{7} = \frac{2}{14}$, we will follow these steps:

• Step 1: Subtract $\frac{3}{7}$ from both sides of the equation to isolate the term with $x$.
• Step 2: Simplify the resulting equation.
• Step 3: Solve for $x$ by multiplying both sides by the reciprocal of the coefficient of $x$.

Now, let's work through the solution:

Step 1: Subtract $\frac{3}{7}$ from both sides:

$\frac{4}{5}x = \frac{2}{14} - \frac{3}{7}$

Step 2: Simplify the right side:

$\frac{2}{14}$ can be simplified to $\frac{1}{7}$, so the equation becomes:

$\frac{4}{5}x = \frac{1}{7} - \frac{3}{7}$

Simplifying the right side gives:

$\frac{4}{5}x = -\frac{2}{7}$

Step 3: Solve for $x$.

Multiply both sides by the reciprocal of $\frac{4}{5}$, which is $\frac{5}{4}$:

$x = -\frac{2}{7} \times \frac{5}{4}$

Perform the multiplication on the right side:

$x = -\frac{2 \times 5}{7 \times 4} = -\frac{10}{28}$

Simplify $-\frac{10}{28}$ by dividing the numerator and the denominator by their greatest common divisor, which is 2:

$x = -\frac{5}{14}$

Thus, the solution to the equation is $x = -\frac{5}{14}$.