Solve 3(2x+1)/5-2(7x-2)/3

$$\frac { 3 ( 2 x + 1 ) } { 5 } - \frac { 2 ( 7 x - 2 ) } { 3 }$$

Evaluate

$$\frac{29-52x}{15}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{3\left(2x+1\right)}{5} times \frac{3}{3}. Multiply \frac{2\left(7x-2\right)}{3} times \frac{5}{5}.

$$\frac{3\times 3\left(2x+1\right)}{15}-\frac{5\times 2\left(7x-2\right)}{15}$$

Since \frac{3\times 3\left(2x+1\right)}{15} and \frac{5\times 2\left(7x-2\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3\left(2x+1\right)-5\times 2\left(7x-2\right)}{15}$$

Do the multiplications in 3\times 3\left(2x+1\right)-5\times 2\left(7x-2\right).

$$\frac{18x+9-70x+20}{15}$$

Combine like terms in 18x+9-70x+20.

$$\frac{-52x+29}{15}$$

Expand

$$\frac{29-52x}{15}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{3\left(2x+1\right)}{5} times \frac{3}{3}. Multiply \frac{2\left(7x-2\right)}{3} times \frac{5}{5}.

$$\frac{3\times 3\left(2x+1\right)}{15}-\frac{5\times 2\left(7x-2\right)}{15}$$

Since \frac{3\times 3\left(2x+1\right)}{15} and \frac{5\times 2\left(7x-2\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3\left(2x+1\right)-5\times 2\left(7x-2\right)}{15}$$

Do the multiplications in 3\times 3\left(2x+1\right)-5\times 2\left(7x-2\right).

$$\frac{18x+9-70x+20}{15}$$

Combine like terms in 18x+9-70x+20.

$$\frac{-52x+29}{15}$$