Solve -6left(-a+8b-7c/4right)

$$-6 \left( -a+8b-7 \frac{ c }{ 4 } \right)$$

Evaluate

$$\frac{21c}{2}+6a-48b$$

Short Solution Steps

Express 7\times \frac{c}{4} as a single fraction.

$$-6\left(-a+8b-\frac{7c}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a+8b times \frac{4}{4}.

$$-6\left(\frac{4\left(-a+8b\right)}{4}-\frac{7c}{4}\right)$$

Since \frac{4\left(-a+8b\right)}{4} and \frac{7c}{4} have the same denominator, subtract them by subtracting their numerators.

$$-6\times \frac{4\left(-a+8b\right)-7c}{4}$$

Do the multiplications in 4\left(-a+8b\right)-7c.

$$-6\times \frac{-4a+32b-7c}{4}$$

Express -6\times \frac{-4a+32b-7c}{4} as a single fraction.

$$\frac{-6\left(-4a+32b-7c\right)}{4}$$

Divide -6\left(-4a+32b-7c\right) by 4 to get -\frac{3}{2}\left(-4a+32b-7c\right).

$$-\frac{3}{2}\left(-4a+32b-7c\right)$$

Use the distributive property to multiply -\frac{3}{2} by -4a+32b-7c.

$$-\frac{3}{2}\left(-4\right)a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\left(-4\right) as a single fraction.

$$\frac{-3\left(-4\right)}{2}a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Multiply -3 and -4 to get 12.

$$\frac{12}{2}a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Divide 12 by 2 to get 6.

$$6a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\times 32 as a single fraction.

$$6a+\frac{-3\times 32}{2}b-\frac{3}{2}\left(-7\right)c$$

Multiply -3 and 32 to get -96.

$$6a+\frac{-96}{2}b-\frac{3}{2}\left(-7\right)c$$

Divide -96 by 2 to get -48.

$$6a-48b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\left(-7\right) as a single fraction.

$$6a-48b+\frac{-3\left(-7\right)}{2}c$$

Multiply -3 and -7 to get 21.

$$6a-48b+\frac{21}{2}c$$

Expand

$$\frac{21c}{2}+6a-48b$$

Short Solution Steps

Express 7\times \frac{c}{4} as a single fraction.

$$-6\left(-a+8b-\frac{7c}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a+8b times \frac{4}{4}.

$$-6\left(\frac{4\left(-a+8b\right)}{4}-\frac{7c}{4}\right)$$

Since \frac{4\left(-a+8b\right)}{4} and \frac{7c}{4} have the same denominator, subtract them by subtracting their numerators.

$$-6\times \frac{4\left(-a+8b\right)-7c}{4}$$

Do the multiplications in 4\left(-a+8b\right)-7c.

$$-6\times \frac{-4a+32b-7c}{4}$$

Express -6\times \frac{-4a+32b-7c}{4} as a single fraction.

$$\frac{-6\left(-4a+32b-7c\right)}{4}$$

Divide -6\left(-4a+32b-7c\right) by 4 to get -\frac{3}{2}\left(-4a+32b-7c\right).

$$-\frac{3}{2}\left(-4a+32b-7c\right)$$

Use the distributive property to multiply -\frac{3}{2} by -4a+32b-7c.

$$-\frac{3}{2}\left(-4\right)a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\left(-4\right) as a single fraction.

$$\frac{-3\left(-4\right)}{2}a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Multiply -3 and -4 to get 12.

$$\frac{12}{2}a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Divide 12 by 2 to get 6.

$$6a-\frac{3}{2}\times 32b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\times 32 as a single fraction.

$$6a+\frac{-3\times 32}{2}b-\frac{3}{2}\left(-7\right)c$$

Multiply -3 and 32 to get -96.

$$6a+\frac{-96}{2}b-\frac{3}{2}\left(-7\right)c$$

Divide -96 by 2 to get -48.

$$6a-48b-\frac{3}{2}\left(-7\right)c$$

Express -\frac{3}{2}\left(-7\right) as a single fraction.

$$6a-48b+\frac{-3\left(-7\right)}{2}c$$

Multiply -3 and -7 to get 21.

$$6a-48b+\frac{21}{2}c$$