Solve 30-34/40-x=34-50/x-45

$$\frac{ 30-34 }{ 40-x } = \frac{ 34-50 }{ x-45 }$$

Solve for x

$$x=41$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 40,45 since division by zero is not defined. Multiply both sides of the equation by \left(x-45\right)\left(x-40\right), the least common multiple of 40-x,x-45.

$$\left(45-x\right)\left(30-34\right)=\left(x-40\right)\left(34-50\right)$$

Subtract 34 from 30 to get -4.

$$\left(45-x\right)\left(-4\right)=\left(x-40\right)\left(34-50\right)$$

Use the distributive property to multiply 45-x by -4.

$$-180+4x=\left(x-40\right)\left(34-50\right)$$

Subtract 50 from 34 to get -16.

$$-180+4x=\left(x-40\right)\left(-16\right)$$

Use the distributive property to multiply x-40 by -16.

$$-180+4x=-16x+640$$

Add 16x to both sides.

$$-180+4x+16x=640$$

Combine 4x and 16x to get 20x.

$$-180+20x=640$$

Add 180 to both sides.

$$20x=640+180$$

Add 640 and 180 to get 820.

$$20x=820$$

Divide both sides by 20.

$$x=\frac{820}{20}$$

Divide 820 by 20 to get 41.

$$x=41$$