Solve x+1/3(x-21/3(5-6x))=5/3(1-9x/3)

$$x + 1 / 3 ( x - 2 \frac { 1 } { 3 } ( 5 - 6 x ) ) = \frac { 5 } { 3 } ( 1 - \frac { 9 x } { 3 } )$$

Solve for x

$$x=\frac{50}{99}\approx 0.505050505$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

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

Multiply 2 and 3 to get 6.

$$3x+1\left(x-\frac{6+1}{3}\left(5-6x\right)\right)=5\left(1-\frac{9x}{3}\right)$$

Add 6 and 1 to get 7.

$$3x+1\left(x-\frac{7}{3}\left(5-6x\right)\right)=5\left(1-\frac{9x}{3}\right)$$

Use the distributive property to multiply -\frac{7}{3} by 5-6x.

$$3x+1\left(x-\frac{7}{3}\times 5-\frac{7}{3}\left(-6\right)x\right)=5\left(1-\frac{9x}{3}\right)$$

Express -\frac{7}{3}\times 5 as a single fraction.

$$3x+1\left(x+\frac{-7\times 5}{3}-\frac{7}{3}\left(-6\right)x\right)=5\left(1-\frac{9x}{3}\right)$$

Multiply -7 and 5 to get -35.

$$3x+1\left(x+\frac{-35}{3}-\frac{7}{3}\left(-6\right)x\right)=5\left(1-\frac{9x}{3}\right)$$

Fraction \frac{-35}{3} can be rewritten as -\frac{35}{3} by extracting the negative sign.

$$3x+1\left(x-\frac{35}{3}-\frac{7}{3}\left(-6\right)x\right)=5\left(1-\frac{9x}{3}\right)$$

Express -\frac{7}{3}\left(-6\right) as a single fraction.

$$3x+1\left(x-\frac{35}{3}+\frac{-7\left(-6\right)}{3}x\right)=5\left(1-\frac{9x}{3}\right)$$

Multiply -7 and -6 to get 42.

$$3x+1\left(x-\frac{35}{3}+\frac{42}{3}x\right)=5\left(1-\frac{9x}{3}\right)$$

Divide 42 by 3 to get 14.

$$3x+1\left(x-\frac{35}{3}+14x\right)=5\left(1-\frac{9x}{3}\right)$$

Combine x and 14x to get 15x.

$$3x+1\left(15x-\frac{35}{3}\right)=5\left(1-\frac{9x}{3}\right)$$

Use the distributive property to multiply 1 by 15x-\frac{35}{3}.

$$3x+15x-\frac{35}{3}=5\left(1-\frac{9x}{3}\right)$$

Combine 3x and 15x to get 18x.

$$18x-\frac{35}{3}=5\left(1-\frac{9x}{3}\right)$$

Divide 9x by 3 to get 3x.

$$18x-\frac{35}{3}=5\left(1-3x\right)$$

Use the distributive property to multiply 5 by 1-3x.

$$18x-\frac{35}{3}=5+5\left(-3x\right)$$

Subtract 5\left(-3x\right) from both sides.

$$18x-\frac{35}{3}-5\left(-3x\right)=5$$

Multiply -1 and 5 to get -5.

$$18x-\frac{35}{3}-5\left(-1\right)\times 3x=5$$

Multiply -5 and -1 to get 5.

$$18x-\frac{35}{3}+5\times 3x=5$$

Multiply 5 and 3 to get 15.

$$18x-\frac{35}{3}+15x=5$$

Combine 18x and 15x to get 33x.

$$33x-\frac{35}{3}=5$$

Add \frac{35}{3} to both sides.

$$33x=5+\frac{35}{3}$$

Convert 5 to fraction \frac{15}{3}.

$$33x=\frac{15}{3}+\frac{35}{3}$$

Since \frac{15}{3} and \frac{35}{3} have the same denominator, add them by adding their numerators.

$$33x=\frac{15+35}{3}$$

Add 15 and 35 to get 50.

$$33x=\frac{50}{3}$$

Divide both sides by 33.

$$x=\frac{\frac{50}{3}}{33}$$

Express \frac{\frac{50}{3}}{33} as a single fraction.

$$x=\frac{50}{3\times 33}$$

Multiply 3 and 33 to get 99.

$$x=\frac{50}{99}$$