Solve x/5-1/7+3x/8=

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

Evaluate

$$\frac{23x}{40}-\frac{1}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 7 is 35. Multiply \frac{x}{5} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{5}{5}.

$$\frac{7x}{35}-\frac{5}{35}+\frac{3x}{8}$$

Since \frac{7x}{35} and \frac{5}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7x-5}{35}+\frac{3x}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 35 and 8 is 280. Multiply \frac{7x-5}{35} times \frac{8}{8}. Multiply \frac{3x}{8} times \frac{35}{35}.

$$\frac{8\left(7x-5\right)}{280}+\frac{35\times 3x}{280}$$

Since \frac{8\left(7x-5\right)}{280} and \frac{35\times 3x}{280} have the same denominator, add them by adding their numerators.

$$\frac{8\left(7x-5\right)+35\times 3x}{280}$$

Do the multiplications in 8\left(7x-5\right)+35\times 3x.

$$\frac{56x-40+105x}{280}$$

Combine like terms in 56x-40+105x.

$$\frac{161x-40}{280}$$

Factor

$$\frac{161x-40}{280}$$

Solution Steps

Factor out \frac{1}{280}.

$$\frac{56x-40+105x}{280}$$

Consider 56x-40+105x. Multiply and combine like terms.

$$161x-40$$

Rewrite the complete factored expression.

$$\frac{161x-40}{280}$$