Solve (x+2):(3x-4)=3:7

$$( x + 2 ) : ( 3 x - 4 ) = 3 : 7$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 7\left(3x-4\right), the least common multiple of 3x-4,7.

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

Use the distributive property to multiply 7 by x+2.

$$7x+14=3\left(3x-4\right)$$

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

$$7x+14=9x-12$$

Subtract 9x from both sides.

$$7x+14-9x=-12$$

Combine 7x and -9x to get -2x.

$$-2x+14=-12$$

Subtract 14 from both sides.

$$-2x=-12-14$$

Subtract 14 from -12 to get -26.

$$-2x=-26$$

Divide both sides by -2.

$$x=\frac{-26}{-2}$$

Divide -26 by -2 to get 13.

$$x=13$$