Solve 31/2k+41/3=72/9

$$3 \frac{ 1 }{ 2 } k+4 \frac{ 1 }{ 3 } = 7 \frac{ 2 }{ 9 }$$

Solve for k

$$k=\frac{52}{63}\approx 0.825396825$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 2,3,9.

$$9\left(3\times 2+1\right)k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Multiply 3 and 2 to get 6.

$$9\left(6+1\right)k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Add 6 and 1 to get 7.

$$9\times 7k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Multiply 9 and 7 to get 63.

$$63k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Multiply 4 and 3 to get 12.

$$63k+6\left(12+1\right)=2\left(7\times 9+2\right)$$

Add 12 and 1 to get 13.

$$63k+6\times 13=2\left(7\times 9+2\right)$$

Multiply 6 and 13 to get 78.

$$63k+78=2\left(7\times 9+2\right)$$

Multiply 7 and 9 to get 63.

$$63k+78=2\left(63+2\right)$$

Add 63 and 2 to get 65.

$$63k+78=2\times 65$$

Multiply 2 and 65 to get 130.

$$63k+78=130$$

Subtract 78 from both sides.

$$63k=130-78$$

Subtract 78 from 130 to get 52.

$$63k=52$$

Divide both sides by 63.

$$k=\frac{52}{63}$$