Solve 4(3+2p)-3(5-p/6)

$$4 ( 3 + 2 p ) - 3 ( 5 - \frac { p } { 6 } )$$

Evaluate

$$\frac{17p}{2}-3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{6}{6}.

$$4\left(3+2p\right)-3\left(\frac{5\times 6}{6}-\frac{p}{6}\right)$$

Since \frac{5\times 6}{6} and \frac{p}{6} have the same denominator, subtract them by subtracting their numerators.

$$4\left(3+2p\right)-3\times \frac{5\times 6-p}{6}$$

Do the multiplications in 5\times 6-p.

$$4\left(3+2p\right)-3\times \frac{30-p}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$4\left(3+2p\right)-\frac{30-p}{2}$$

Use the distributive property to multiply 4 by 3+2p.

$$12+8p-\frac{30-p}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12+8p times \frac{2}{2}.

$$\frac{2\left(12+8p\right)}{2}-\frac{30-p}{2}$$

Since \frac{2\left(12+8p\right)}{2} and \frac{30-p}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(12+8p\right)-\left(30-p\right)}{2}$$

Do the multiplications in 2\left(12+8p\right)-\left(30-p\right).

$$\frac{24+16p-30+p}{2}$$

Combine like terms in 24+16p-30+p.

$$\frac{-6+17p}{2}$$

Expand

$$\frac{17p}{2}-3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{6}{6}.

$$4\left(3+2p\right)-3\left(\frac{5\times 6}{6}-\frac{p}{6}\right)$$

Since \frac{5\times 6}{6} and \frac{p}{6} have the same denominator, subtract them by subtracting their numerators.

$$4\left(3+2p\right)-3\times \frac{5\times 6-p}{6}$$

Do the multiplications in 5\times 6-p.

$$4\left(3+2p\right)-3\times \frac{30-p}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$4\left(3+2p\right)-\frac{30-p}{2}$$

Use the distributive property to multiply 4 by 3+2p.

$$12+8p-\frac{30-p}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12+8p times \frac{2}{2}.

$$\frac{2\left(12+8p\right)}{2}-\frac{30-p}{2}$$

Since \frac{2\left(12+8p\right)}{2} and \frac{30-p}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(12+8p\right)-\left(30-p\right)}{2}$$

Do the multiplications in 2\left(12+8p\right)-\left(30-p\right).

$$\frac{24+16p-30+p}{2}$$

Combine like terms in 24+16p-30+p.

$$\frac{-6+17p}{2}$$