Solve 21-15/35-x=21-30/x-40

$$\frac{ 21-15 }{ 35-x } = \frac{ 21-30 }{ x-40 }$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 35,40 since division by zero is not defined. Multiply both sides of the equation by \left(x-40\right)\left(x-35\right), the least common multiple of 35-x,x-40.

$$\left(40-x\right)\left(21-15\right)=\left(x-35\right)\left(21-30\right)$$

Subtract 15 from 21 to get 6.

$$\left(40-x\right)\times 6=\left(x-35\right)\left(21-30\right)$$

Use the distributive property to multiply 40-x by 6.

$$240-6x=\left(x-35\right)\left(21-30\right)$$

Subtract 30 from 21 to get -9.

$$240-6x=\left(x-35\right)\left(-9\right)$$

Use the distributive property to multiply x-35 by -9.

$$240-6x=-9x+315$$

Add 9x to both sides.

$$240-6x+9x=315$$

Combine -6x and 9x to get 3x.

$$240+3x=315$$

Subtract 240 from both sides.

$$3x=315-240$$

Subtract 240 from 315 to get 75.

$$3x=75$$

Divide both sides by 3.

$$x=\frac{75}{3}$$

Divide 75 by 3 to get 25.

$$x=25$$