Solve (x-4)/(-3x+1)=-14/19

$$\frac { ( x - 4 ) } { ( - 3 x + 1 ) } = \frac { - 14 } { 19 }$$

Solve for x

$$x = -\frac{62}{23} = -2\frac{16}{23} \approx -2.695652174$$

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 19\left(3x-1\right), the least common multiple of -3x+1,19.

$$-19\left(x-4\right)=\left(3x-1\right)\left(-14\right)$$

Use the distributive property to multiply -19 by x-4.

$$-19x+76=\left(3x-1\right)\left(-14\right)$$

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

$$-19x+76=-42x+14$$

Add 42x to both sides.

$$-19x+76+42x=14$$

Combine -19x and 42x to get 23x.

$$23x+76=14$$

Subtract 76 from both sides.

$$23x=14-76$$

Subtract 76 from 14 to get -62.

$$23x=-62$$

Divide both sides by 23.

$$x=\frac{-62}{23}$$

Fraction \frac{-62}{23} can be rewritten as -\frac{62}{23} by extracting the negative sign.

$$x=-\frac{62}{23}$$