Solve 23-x/30-x=57-x/78-x

$$\frac { 23 - x } { 30 - x } = \frac { 57 - x } { 78 - x }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 30,78 since division by zero is not defined. Multiply both sides of the equation by \left(x-78\right)\left(x-30\right), the least common multiple of 30-x,78-x.

$$\left(78-x\right)\left(23-x\right)=\left(30-x\right)\left(57-x\right)$$

Use the distributive property to multiply 78-x by 23-x and combine like terms.

$$1794-101x+x^{2}=\left(30-x\right)\left(57-x\right)$$

Use the distributive property to multiply 30-x by 57-x and combine like terms.

$$1794-101x+x^{2}=1710-87x+x^{2}$$

Add 87x to both sides.

$$1794-101x+x^{2}+87x=1710+x^{2}$$

Combine -101x and 87x to get -14x.

$$1794-14x+x^{2}=1710+x^{2}$$

Subtract x^{2} from both sides.

$$1794-14x+x^{2}-x^{2}=1710$$

Combine x^{2} and -x^{2} to get 0.

$$1794-14x=1710$$

Subtract 1794 from both sides.

$$-14x=1710-1794$$

Subtract 1794 from 1710 to get -84.

$$-14x=-84$$

Divide both sides by -14.

$$x=\frac{-84}{-14}$$

Divide -84 by -14 to get 6.

$$x=6$$