Solve 2/8(11/9x+3/5)-4/5(frac{5}{19}x-frac{1}{9})=1frac{8}{5}

$$\frac { 2 } { 8 } ( 1 \frac { 1 } { 9 } x + \frac { 3 } { 5 } ) - \frac { 4 } { 5 } ( \frac { 5 } { 19 } x - \frac { 1 } { 9 } ) = 1 \frac { 8 } { 5 }$$

Solve for x

$$x = \frac{1615}{46} = 35\frac{5}{46} \approx 35.108695652$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6840, the least common multiple of 8,9,5,19.

$$1710\left(\frac{1\times 9+1}{9}x+\frac{3}{5}\right)-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Multiply 1 and 9 to get 9.

$$1710\left(\frac{9+1}{9}x+\frac{3}{5}\right)-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Add 9 and 1 to get 10.

$$1710\left(\frac{10}{9}x+\frac{3}{5}\right)-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Use the distributive property to multiply 1710 by \frac{10}{9}x+\frac{3}{5}.

$$1710\times \frac{10}{9}x+1710\times \frac{3}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Express 1710\times \frac{10}{9} as a single fraction.

$$\frac{1710\times 10}{9}x+1710\times \frac{3}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Multiply 1710 and 10 to get 17100.

$$\frac{17100}{9}x+1710\times \frac{3}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Divide 17100 by 9 to get 1900.

$$1900x+1710\times \frac{3}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Express 1710\times \frac{3}{5} as a single fraction.

$$1900x+\frac{1710\times 3}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Multiply 1710 and 3 to get 5130.

$$1900x+\frac{5130}{5}-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Divide 5130 by 5 to get 1026.

$$1900x+1026-5472\left(\frac{5}{19}x-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Use the distributive property to multiply -5472 by \frac{5}{19}x-\frac{1}{9}.

$$1900x+1026-5472\times \frac{5}{19}x-5472\left(-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Express -5472\times \frac{5}{19} as a single fraction.

$$1900x+1026+\frac{-5472\times 5}{19}x-5472\left(-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Multiply -5472 and 5 to get -27360.

$$1900x+1026+\frac{-27360}{19}x-5472\left(-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Divide -27360 by 19 to get -1440.

$$1900x+1026-1440x-5472\left(-\frac{1}{9}\right)=1368\left(1\times 5+8\right)$$

Express -5472\left(-\frac{1}{9}\right) as a single fraction.

$$1900x+1026-1440x+\frac{-5472\left(-1\right)}{9}=1368\left(1\times 5+8\right)$$

Multiply -5472 and -1 to get 5472.

$$1900x+1026-1440x+\frac{5472}{9}=1368\left(1\times 5+8\right)$$

Divide 5472 by 9 to get 608.

$$1900x+1026-1440x+608=1368\left(1\times 5+8\right)$$

Combine 1900x and -1440x to get 460x.

$$460x+1026+608=1368\left(1\times 5+8\right)$$

Add 1026 and 608 to get 1634.

$$460x+1634=1368\left(1\times 5+8\right)$$

Multiply 1 and 5 to get 5.

$$460x+1634=1368\left(5+8\right)$$

Add 5 and 8 to get 13.

$$460x+1634=1368\times 13$$

Multiply 1368 and 13 to get 17784.

$$460x+1634=17784$$

Subtract 1634 from both sides.

$$460x=17784-1634$$

Subtract 1634 from 17784 to get 16150.

$$460x=16150$$

Divide both sides by 460.

$$x=\frac{16150}{460}$$

Reduce the fraction \frac{16150}{460} to lowest terms by extracting and canceling out 10.

$$x=\frac{1615}{46}$$