Solve 2/3x-55/6y+1/2x-(-21/3y)-4frac{5}{12}-sqrt{36}

$$\frac { 2 } { 3 } x - 5 \frac { 5 } { 6 } y + \frac { 1 } { 2 } x - ( - 2 \frac { 1 } { 3 } y ) - 4 \frac { 5 } { 12 } - \sqrt { 36 }$$

Evaluate

$$\frac{7x}{6}-\frac{7y}{2}-\frac{125}{12}$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{2}{3}x-\frac{30+5}{6}y+\frac{1}{2}x-\left(-\frac{2\times 3+1}{3}\right)y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Add 30 and 5 to get 35.

$$\frac{2}{3}x-\frac{35}{6}y+\frac{1}{2}x-\left(-\frac{2\times 3+1}{3}\right)y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Combine \frac{2}{3}x and \frac{1}{2}x to get \frac{7}{6}x.

$$\frac{7}{6}x-\frac{35}{6}y-\left(-\frac{2\times 3+1}{3}\right)y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{6}x-\frac{35}{6}y-\left(-\frac{6+1}{3}\right)y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Add 6 and 1 to get 7.

$$\frac{7}{6}x-\frac{35}{6}y-\left(-\frac{7}{3}y\right)-\frac{4\times 12+5}{12}-\sqrt{36}$$

The opposite of -\frac{7}{3}y is \frac{7}{3}y.

$$\frac{7}{6}x-\frac{35}{6}y+\frac{7}{3}y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Combine -\frac{35}{6}y and \frac{7}{3}y to get -\frac{7}{2}y.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{4\times 12+5}{12}-\sqrt{36}$$

Multiply 4 and 12 to get 48.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{48+5}{12}-\sqrt{36}$$

Add 48 and 5 to get 53.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{53}{12}-\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{53}{12}-6$$

Convert 6 to fraction \frac{72}{12}.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{53}{12}-\frac{72}{12}$$

Since -\frac{53}{12} and \frac{72}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}x-\frac{7}{2}y+\frac{-53-72}{12}$$

Subtract 72 from -53 to get -125.

$$\frac{7}{6}x-\frac{7}{2}y-\frac{125}{12}$$

Factor

$$\frac{14x-42y-125}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{14x-42y-125}{12}$$