Solve 8x-2/3+5x+2/5

$$8 \frac { x - 2 } { 3 } + \frac { 5 x + 2 } { 5 }$$

Evaluate

$$\frac{11x}{3}-\frac{74}{15}$$

Short Solution Steps

Express 8\times \frac{x-2}{3} as a single fraction.

$$\frac{8\left(x-2\right)}{3}+\frac{5x+2}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{8\left(x-2\right)}{3} times \frac{5}{5}. Multiply \frac{5x+2}{5} times \frac{3}{3}.

$$\frac{5\times 8\left(x-2\right)}{15}+\frac{3\left(5x+2\right)}{15}$$

Since \frac{5\times 8\left(x-2\right)}{15} and \frac{3\left(5x+2\right)}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\times 8\left(x-2\right)+3\left(5x+2\right)}{15}$$

Do the multiplications in 5\times 8\left(x-2\right)+3\left(5x+2\right).

$$\frac{40x-80+15x+6}{15}$$

Combine like terms in 40x-80+15x+6.

$$\frac{55x-74}{15}$$

Expand

$$\frac{11x}{3}-\frac{74}{15}$$

Short Solution Steps

Express 8\times \frac{x-2}{3} as a single fraction.

$$\frac{8\left(x-2\right)}{3}+\frac{5x+2}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{8\left(x-2\right)}{3} times \frac{5}{5}. Multiply \frac{5x+2}{5} times \frac{3}{3}.

$$\frac{5\times 8\left(x-2\right)}{15}+\frac{3\left(5x+2\right)}{15}$$

Since \frac{5\times 8\left(x-2\right)}{15} and \frac{3\left(5x+2\right)}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\times 8\left(x-2\right)+3\left(5x+2\right)}{15}$$

Do the multiplications in 5\times 8\left(x-2\right)+3\left(5x+2\right).

$$\frac{40x-80+15x+6}{15}$$

Combine like terms in 40x-80+15x+6.

$$\frac{55x-74}{15}$$