Solve (x-4)/(-3x+1)=-14/9

$$\frac { ( x - 4 ) } { ( - 3 x + 1 ) } = - \frac { 14 } { 9 }$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 9\left(3x-1\right), the least common multiple of -3x+1,9.

$$-9\left(x-4\right)=-14\left(3x-1\right)$$

Use the distributive property to multiply -9 by x-4.

$$-9x+36=-14\left(3x-1\right)$$

Use the distributive property to multiply -14 by 3x-1.

$$-9x+36=-42x+14$$

Add 42x to both sides.

$$-9x+36+42x=14$$

Combine -9x and 42x to get 33x.

$$33x+36=14$$

Subtract 36 from both sides.

$$33x=14-36$$

Subtract 36 from 14 to get -22.

$$33x=-22$$

Divide both sides by 33.

$$x=\frac{-22}{33}$$

Reduce the fraction \frac{-22}{33} to lowest terms by extracting and canceling out 11.

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