Solve for x x-(x-1)/3-(2x-5)/5+(x+8)/6=7

$x - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1

Simplify $x - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6}$ .

Find the common denominator.

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Multiply $\frac{x}{1}$ by $\frac{30}{30}$ .

$\frac{x}{1} \cdot \frac{30}{30} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Multiply $\frac{x}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 30}{30} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Multiply $\frac{x - 1}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 30}{30} - (\frac{x - 1}{3} \cdot \frac{10}{10}) - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Multiply $\frac{x - 1}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Multiply $\frac{2 x - 5}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - (\frac{2 x - 5}{5} \cdot \frac{6}{6}) + \frac{x + 8}{6} = 7$

Multiply $\frac{2 x - 5}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{x + 8}{6} = 7$

Multiply $\frac{x + 8}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{x + 8}{6} \cdot \frac{5}{5} = 7$

Multiply $\frac{x + 8}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Multiply $3$ by $10$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Multiply $5$ by $6$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Reorder the factors of $6 \cdot 5$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{5 \cdot 6} = 7$

Multiply $5$ by $6$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{30} = 7$

Combine the numerators over the common denominator.

$\frac{x \cdot 30 - (x - 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Simplify each term.

Move $30$ to the left of $x$ .

$\frac{30 \cdot x - (x - 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$