Solve 6z-5/9-2(3z+1)/5+2z

$$\frac { 6 z - 5 } { 9 } - \frac { 2 ( 3 z + 1 ) } { 5 } + 2 z$$

Evaluate

$$\frac{22z}{15}-\frac{43}{45}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 5 is 45. Multiply \frac{6z-5}{9} times \frac{5}{5}. Multiply \frac{2\left(3z+1\right)}{5} times \frac{9}{9}.

$$\frac{5\left(6z-5\right)}{45}-\frac{9\times 2\left(3z+1\right)}{45}+2z$$

Since \frac{5\left(6z-5\right)}{45} and \frac{9\times 2\left(3z+1\right)}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(6z-5\right)-9\times 2\left(3z+1\right)}{45}+2z$$

Do the multiplications in 5\left(6z-5\right)-9\times 2\left(3z+1\right).

$$\frac{30z-25-54z-18}{45}+2z$$

Combine like terms in 30z-25-54z-18.

$$\frac{-24z-43}{45}+2z$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2z times \frac{45}{45}.

$$\frac{-24z-43}{45}+\frac{45\times 2z}{45}$$

Since \frac{-24z-43}{45} and \frac{45\times 2z}{45} have the same denominator, add them by adding their numerators.

$$\frac{-24z-43+45\times 2z}{45}$$

Do the multiplications in -24z-43+45\times 2z.

$$\frac{-24z-43+90z}{45}$$

Combine like terms in -24z-43+90z.

$$\frac{66z-43}{45}$$

Expand

$$\frac{22z}{15}-\frac{43}{45}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 5 is 45. Multiply \frac{6z-5}{9} times \frac{5}{5}. Multiply \frac{2\left(3z+1\right)}{5} times \frac{9}{9}.

$$\frac{5\left(6z-5\right)}{45}-\frac{9\times 2\left(3z+1\right)}{45}+2z$$

Since \frac{5\left(6z-5\right)}{45} and \frac{9\times 2\left(3z+1\right)}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(6z-5\right)-9\times 2\left(3z+1\right)}{45}+2z$$

Do the multiplications in 5\left(6z-5\right)-9\times 2\left(3z+1\right).

$$\frac{30z-25-54z-18}{45}+2z$$

Combine like terms in 30z-25-54z-18.

$$\frac{-24z-43}{45}+2z$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2z times \frac{45}{45}.

$$\frac{-24z-43}{45}+\frac{45\times 2z}{45}$$

Since \frac{-24z-43}{45} and \frac{45\times 2z}{45} have the same denominator, add them by adding their numerators.

$$\frac{-24z-43+45\times 2z}{45}$$

Do the multiplications in -24z-43+45\times 2z.

$$\frac{-24z-43+90z}{45}$$

Combine like terms in -24z-43+90z.

$$\frac{66z-43}{45}$$