Solve sqrt{9/4}-(6/7-7)+[2-1/2-(7-1/2)]+(frac{1}{3})^-1

$$\sqrt { \frac { 9 } { 4 } } - ( \frac { 6 } { 7 } - 7 ) + [ 2 - \frac { 1 } { 2 } - ( 7 - \frac { 1 } { 2 } ) ] + ( \frac { 1 } { 3 } ) ^ { - 1 }$$

Evaluate

$$\frac{79}{14}\approx 5.642857143$$

Solution Steps

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}-\left(\frac{6}{7}-7\right)+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+\left(\frac{1}{3}\right)^{-1}$$

Subtract 7 from \frac{6}{7} to get -\frac{43}{7}.

$$\frac{3}{2}-\left(-\frac{43}{7}\right)+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+\left(\frac{1}{3}\right)^{-1}$$

The opposite of -\frac{43}{7} is \frac{43}{7}.

$$\frac{3}{2}+\frac{43}{7}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+\left(\frac{1}{3}\right)^{-1}$$

Add \frac{3}{2} and \frac{43}{7} to get \frac{107}{14}.

$$\frac{107}{14}+2-\frac{1}{2}-\left(7-\frac{1}{2}\right)+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

$$\frac{107}{14}+\frac{3}{2}-\left(7-\frac{1}{2}\right)+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{1}{2} from 7 to get \frac{13}{2}.

$$\frac{107}{14}+\frac{3}{2}-\frac{13}{2}+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{13}{2} from \frac{3}{2} to get -5.

$$\frac{107}{14}-5+\left(\frac{1}{3}\right)^{-1}$$

Subtract 5 from \frac{107}{14} to get \frac{37}{14}.

$$\frac{37}{14}+\left(\frac{1}{3}\right)^{-1}$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$\frac{37}{14}+3$$

Add \frac{37}{14} and 3 to get \frac{79}{14}.

$$\frac{79}{14}$$

Factor

$$\frac{79}{2 \cdot 7} = 5\frac{9}{14} = 5.642857142857143$$