Solve 7(x+4)/3-(7x+42)/2

$$\frac { 7 ( x + 4 ) } { 3 } - \frac { ( 7 x + 42 ) } { 2 }$$

Evaluate

$$-\frac{7x}{6}-\frac{35}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{7\left(x+4\right)}{3} times \frac{2}{2}. Multiply \frac{7x+42}{2} times \frac{3}{3}.

$$\frac{2\times 7\left(x+4\right)}{6}-\frac{3\left(7x+42\right)}{6}$$

Since \frac{2\times 7\left(x+4\right)}{6} and \frac{3\left(7x+42\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 7\left(x+4\right)-3\left(7x+42\right)}{6}$$

Do the multiplications in 2\times 7\left(x+4\right)-3\left(7x+42\right).

$$\frac{14x+56-21x-126}{6}$$

Combine like terms in 14x+56-21x-126.

$$\frac{-7x-70}{6}$$

Expand

$$-\frac{7x}{6}-\frac{35}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{7\left(x+4\right)}{3} times \frac{2}{2}. Multiply \frac{7x+42}{2} times \frac{3}{3}.

$$\frac{2\times 7\left(x+4\right)}{6}-\frac{3\left(7x+42\right)}{6}$$

Since \frac{2\times 7\left(x+4\right)}{6} and \frac{3\left(7x+42\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 7\left(x+4\right)-3\left(7x+42\right)}{6}$$

Do the multiplications in 2\times 7\left(x+4\right)-3\left(7x+42\right).

$$\frac{14x+56-21x-126}{6}$$

Combine like terms in 14x+56-21x-126.

$$\frac{-7x-70}{6}$$