Solve (10-x):x=2:3

$$( 10 - x ) : x = 2 : 3$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.

$$3\left(10-x\right)=2x$$

Use the distributive property to multiply 3 by 10-x.

$$30-3x=2x$$

Subtract 2x from both sides.

$$30-3x-2x=0$$

Combine -3x and -2x to get -5x.

$$30-5x=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$-5x=-30$$

Divide both sides by -5.

$$x=\frac{-30}{-5}$$

Divide -30 by -5 to get 6.

$$x=6$$