Solve the Fraction Equation: 3/8x + 1/5 - 6/10 with Multiple X Terms

To solve the equation $\frac{3}{8}x+\frac{1}{5}-\frac{6}{10}=-\frac{10}{25}+\frac{1}{3}x-\frac{7}{8}x$, we'll proceed with the following steps:

• Step 1: Simplify each side separately.
• Step 2: Combine like terms.
• Step 3: Isolate the variable $x$ and solve.

Let's simplify each side of the equation:

The left side:

$\frac{3}{8}x + \frac{1}{5} - \frac{6}{10}$. Here, $\frac{6}{10} = \frac{3}{5}$.

Thus, the left side becomes $\frac{3}{8}x + \frac{1}{5} - \frac{3}{5} = \frac{3}{8}x - \frac{2}{5}$.

The right side:

$-\frac{10}{25} + \frac{1}{3}x - \frac{7}{8}x$. First simplify the constant term: $-\frac{10}{25} = -\frac{2}{5}$.

Combine like terms involving $x$: $\frac{1}{3}x - \frac{7}{8}x = \left(\frac{1}{3} - \frac{7}{8}\right)x$.

To combine the terms, find a common denominator (24), and we get:

$\frac{1}{3} = \frac{8}{24}$ and $\frac{7}{8} = \frac{21}{24}$.

Thus, $\frac{8}{24}x - \frac{21}{24}x = -\frac{13}{24}x$.

So, the right side simplifies to $-\frac{2}{5} - \frac{13}{24}x$.

Overall equation now is:

$\frac{3}{8}x - \frac{2}{5} = -\frac{2}{5} - \frac{13}{24}x$.

Add $\frac{13}{24}x$ to both sides to collect all terms involving $x$ on one side:

$\frac{3}{8}x + \frac{13}{24}x = -\frac{2}{5} + \frac{2}{5}$.

The right side is zero, so the left side becomes:

$\frac{3}{8}x + \frac{13}{24}x$ requires finding a common denominator (24):

$\frac{3}{8}x = \frac{9}{24}x$.

Thus, it becomes: $\frac{9}{24}x + \frac{13}{24}x = \frac{22}{24}x = 0$.

Since $\frac{22}{24}x = 0$, dividing both sides by $\frac{22}{24}$:

$x = 0$.

Therefore, the solution is $x = 0$ , which corresponds to choice 1.