Solve 8varepsilon-3+7/2[2+3(4+9)-8(7-3/8)]

$$8 \varepsilon - 3 + \frac { 7 } { 2 } [ 2 + 3 ( 4 + 9 ) - 8 ( 7 - \frac { 3 } { 8 } ) ]$$

Evaluate

$$8\epsilon -45$$

Solution Steps

Add 4 and 9 to get 13.

$$8\epsilon -3+\frac{7}{2}\left(2+3\times 13-8\left(7-\frac{3}{8}\right)\right)$$

Multiply 3 and 13 to get 39.

$$8\epsilon -3+\frac{7}{2}\left(2+39-8\left(7-\frac{3}{8}\right)\right)$$

Add 2 and 39 to get 41.

$$8\epsilon -3+\frac{7}{2}\left(41-8\left(7-\frac{3}{8}\right)\right)$$

Convert 7 to fraction \frac{56}{8}.

$$8\epsilon -3+\frac{7}{2}\left(41-8\left(\frac{56}{8}-\frac{3}{8}\right)\right)$$

Since \frac{56}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$8\epsilon -3+\frac{7}{2}\left(41-8\times \frac{56-3}{8}\right)$$

Subtract 3 from 56 to get 53.

$$8\epsilon -3+\frac{7}{2}\left(41-8\times \frac{53}{8}\right)$$

Cancel out 8 and 8.

$$8\epsilon -3+\frac{7}{2}\left(41-53\right)$$

Subtract 53 from 41 to get -12.

$$8\epsilon -3+\frac{7}{2}\left(-12\right)$$

Express \frac{7}{2}\left(-12\right) as a single fraction.

$$8\epsilon -3+\frac{7\left(-12\right)}{2}$$

Multiply 7 and -12 to get -84.

$$8\epsilon -3+\frac{-84}{2}$$

Divide -84 by 2 to get -42.

$$8\epsilon -3-42$$

Subtract 42 from -3 to get -45.

$$8\epsilon -45$$

Expand

$$8\epsilon -45$$

Solution Steps

Add 4 and 9 to get 13.

$$8\epsilon -3+\frac{7}{2}\left(2+3\times 13-8\left(7-\frac{3}{8}\right)\right)$$

Multiply 3 and 13 to get 39.

$$8\epsilon -3+\frac{7}{2}\left(2+39-8\left(7-\frac{3}{8}\right)\right)$$

Add 2 and 39 to get 41.

$$8\epsilon -3+\frac{7}{2}\left(41-8\left(7-\frac{3}{8}\right)\right)$$

Convert 7 to fraction \frac{56}{8}.

$$8\epsilon -3+\frac{7}{2}\left(41-8\left(\frac{56}{8}-\frac{3}{8}\right)\right)$$

Since \frac{56}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$8\epsilon -3+\frac{7}{2}\left(41-8\times \frac{56-3}{8}\right)$$

Subtract 3 from 56 to get 53.

$$8\epsilon -3+\frac{7}{2}\left(41-8\times \frac{53}{8}\right)$$

Cancel out 8 and 8.

$$8\epsilon -3+\frac{7}{2}\left(41-53\right)$$

Subtract 53 from 41 to get -12.

$$8\epsilon -3+\frac{7}{2}\left(-12\right)$$

Express \frac{7}{2}\left(-12\right) as a single fraction.

$$8\epsilon -3+\frac{7\left(-12\right)}{2}$$

Multiply 7 and -12 to get -84.

$$8\epsilon -3+\frac{-84}{2}$$

Divide -84 by 2 to get -42.

$$8\epsilon -3-42$$

Subtract 42 from -3 to get -45.

$$8\epsilon -45$$