Solve 3(25/9-x)+211/18=14/9

$$3 ( 2 \frac { 5 } { 9 } - x ) + 2 \frac { 11 } { 18 } = 1 \frac { 4 } { 9 }$$

Solve for x

$$x = \frac{53}{18} = 2\frac{17}{18} \approx 2.944444444$$

Steps for Solving Linear Equation

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

$$54\left(\frac{2\times 9+5}{9}-x\right)+2\times 18+11=2\left(1\times 9+4\right)$$

Multiply 2 and 9 to get 18.

$$54\left(\frac{18+5}{9}-x\right)+2\times 18+11=2\left(1\times 9+4\right)$$

Add 18 and 5 to get 23.

$$54\left(\frac{23}{9}-x\right)+2\times 18+11=2\left(1\times 9+4\right)$$

Use the distributive property to multiply 54 by \frac{23}{9}-x.

$$54\times \frac{23}{9}-54x+2\times 18+11=2\left(1\times 9+4\right)$$

Express 54\times \frac{23}{9} as a single fraction.

$$\frac{54\times 23}{9}-54x+2\times 18+11=2\left(1\times 9+4\right)$$

Multiply 54 and 23 to get 1242.

$$\frac{1242}{9}-54x+2\times 18+11=2\left(1\times 9+4\right)$$

Divide 1242 by 9 to get 138.

$$138-54x+2\times 18+11=2\left(1\times 9+4\right)$$

Multiply 2 and 18 to get 36.

$$138-54x+36+11=2\left(1\times 9+4\right)$$

Add 138 and 36 to get 174.

$$174-54x+11=2\left(1\times 9+4\right)$$

Add 174 and 11 to get 185.

$$185-54x=2\left(1\times 9+4\right)$$

Multiply 1 and 9 to get 9.

$$185-54x=2\left(9+4\right)$$

Add 9 and 4 to get 13.

$$185-54x=2\times 13$$

Multiply 2 and 13 to get 26.

$$185-54x=26$$

Subtract 185 from both sides.

$$-54x=26-185$$

Subtract 185 from 26 to get -159.

$$-54x=-159$$

Divide both sides by -54.

$$x=\frac{-159}{-54}$$

Reduce the fraction \frac{-159}{-54} to lowest terms by extracting and canceling out -3.

$$x=\frac{53}{18}$$