Solve (x-4)/(-3x+1)=-14/6

$$\frac { ( x - 4 ) } { ( - 3 x + 1 ) } = - \frac { 14 } { 6 }$$

Solve for x

$$x=-\frac{5}{18}\approx -0.277777778$$

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 6\left(3x-1\right), the least common multiple of -3x+1,6.

$$-6\left(x-4\right)=-\left(3x-1\right)\times 14$$

Use the distributive property to multiply -6 by x-4.

$$-6x+24=-\left(3x-1\right)\times 14$$

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

$$-6x+24=-\left(42x-14\right)$$

To find the opposite of 42x-14, find the opposite of each term.

$$-6x+24=-42x+14$$

Add 42x to both sides.

$$-6x+24+42x=14$$

Combine -6x and 42x to get 36x.

$$36x+24=14$$

Subtract 24 from both sides.

$$36x=14-24$$

Subtract 24 from 14 to get -10.

$$36x=-10$$

Divide both sides by 36.

$$x=\frac{-10}{36}$$

Reduce the fraction \frac{-10}{36} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{18}$$