Solve 39/45x+17/30x=61/9

$$3 \frac { 9 } { 45 } x + 1 \frac { 7 } { 30 } x = 6 \frac { 1 } { 9 }$$

Solve for x

$$x = \frac{550}{399} = 1\frac{151}{399} \approx 1.378446115$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 45,30,9.

$$2\left(3\times 45+9\right)x+3\left(1\times 30+7\right)x=10\left(6\times 9+1\right)$$

Multiply 3 and 45 to get 135.

$$2\left(135+9\right)x+3\left(1\times 30+7\right)x=10\left(6\times 9+1\right)$$

Add 135 and 9 to get 144.

$$2\times 144x+3\left(1\times 30+7\right)x=10\left(6\times 9+1\right)$$

Multiply 2 and 144 to get 288.

$$288x+3\left(1\times 30+7\right)x=10\left(6\times 9+1\right)$$

Multiply 1 and 30 to get 30.

$$288x+3\left(30+7\right)x=10\left(6\times 9+1\right)$$

Add 30 and 7 to get 37.

$$288x+3\times 37x=10\left(6\times 9+1\right)$$

Multiply 3 and 37 to get 111.

$$288x+111x=10\left(6\times 9+1\right)$$

Combine 288x and 111x to get 399x.

$$399x=10\left(6\times 9+1\right)$$

Multiply 6 and 9 to get 54.

$$399x=10\left(54+1\right)$$

Add 54 and 1 to get 55.

$$399x=10\times 55$$

Multiply 10 and 55 to get 550.

$$399x=550$$

Divide both sides by 399.

$$x=\frac{550}{399}$$