Solve x-1/6[12-6(3/5x-1)]=3/7x-2

$$x - \frac { 1 } { 6 } [ 12 - 6 ( \frac { 3 } { 5 } x - 1 ) ] = \frac { 3 } { 7 } x - 2$$

Solve for x

$$x=\frac{35}{41}\approx 0.853658537$$

Steps for Solving Linear Equation

Use the distributive property to multiply -6 by \frac{3}{5}x-1.

$$x-\frac{1}{6}\left(12-6\times \frac{3}{5}x+6\right)=\frac{3}{7}x-2$$

Express -6\times \frac{3}{5} as a single fraction.

$$x-\frac{1}{6}\left(12+\frac{-6\times 3}{5}x+6\right)=\frac{3}{7}x-2$$

Multiply -6 and 3 to get -18.

$$x-\frac{1}{6}\left(12+\frac{-18}{5}x+6\right)=\frac{3}{7}x-2$$

Fraction \frac{-18}{5} can be rewritten as -\frac{18}{5} by extracting the negative sign.

$$x-\frac{1}{6}\left(12-\frac{18}{5}x+6\right)=\frac{3}{7}x-2$$

Add 12 and 6 to get 18.

$$x-\frac{1}{6}\left(18-\frac{18}{5}x\right)=\frac{3}{7}x-2$$

Use the distributive property to multiply -\frac{1}{6} by 18-\frac{18}{5}x.

$$x-\frac{1}{6}\times 18-\frac{1}{6}\left(-\frac{18}{5}\right)x=\frac{3}{7}x-2$$

Express -\frac{1}{6}\times 18 as a single fraction.

$$x+\frac{-18}{6}-\frac{1}{6}\left(-\frac{18}{5}\right)x=\frac{3}{7}x-2$$

Divide -18 by 6 to get -3.

$$x-3-\frac{1}{6}\left(-\frac{18}{5}\right)x=\frac{3}{7}x-2$$

Multiply -\frac{1}{6} times -\frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$x-3+\frac{-\left(-18\right)}{6\times 5}x=\frac{3}{7}x-2$$

Do the multiplications in the fraction \frac{-\left(-18\right)}{6\times 5}.

$$x-3+\frac{18}{30}x=\frac{3}{7}x-2$$

Reduce the fraction \frac{18}{30} to lowest terms by extracting and canceling out 6.

$$x-3+\frac{3}{5}x=\frac{3}{7}x-2$$

Combine x and \frac{3}{5}x to get \frac{8}{5}x.

$$\frac{8}{5}x-3=\frac{3}{7}x-2$$

Subtract \frac{3}{7}x from both sides.

$$\frac{8}{5}x-3-\frac{3}{7}x=-2$$

Combine \frac{8}{5}x and -\frac{3}{7}x to get \frac{41}{35}x.

$$\frac{41}{35}x-3=-2$$

Add 3 to both sides.

$$\frac{41}{35}x=-2+3$$

Add -2 and 3 to get 1.

$$\frac{41}{35}x=1$$

Multiply both sides by \frac{35}{41}, the reciprocal of \frac{41}{35}.

$$x=1\times \frac{35}{41}$$

Multiply 1 and \frac{35}{41} to get \frac{35}{41}.

$$x=\frac{35}{41}$$