Solve 4(2x-1)/3-x=4/7

$$\frac { 4 ( 2 x - 1 ) } { 3 - x } = \frac { 4 } { 7 }$$

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 7\left(x-3\right), the least common multiple of 3-x,7.

$$-7\times 4\left(2x-1\right)=4\left(x-3\right)$$

Multiply -7 and 4 to get -28.

$$-28\left(2x-1\right)=4\left(x-3\right)$$

Use the distributive property to multiply -28 by 2x-1.

$$-56x+28=4\left(x-3\right)$$

Use the distributive property to multiply 4 by x-3.

$$-56x+28=4x-12$$

Subtract 4x from both sides.

$$-56x+28-4x=-12$$

Combine -56x and -4x to get -60x.

$$-60x+28=-12$$

Subtract 28 from both sides.

$$-60x=-12-28$$

Subtract 28 from -12 to get -40.

$$-60x=-40$$

Divide both sides by -60.

$$x=\frac{-40}{-60}$$

Reduce the fraction \frac{-40}{-60} to lowest terms by extracting and canceling out -20.

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