Solve 30-44/40-x=44-50/x-45

$$\frac{ 30-44 }{ 40-x } = \frac{ 44-50 }{ x-45 }$$

Solve for x

$$x = \frac{87}{2} = 43\frac{1}{2} = 43.5$$

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.

$$\left(45-x\right)\left(30-44\right)=\left(x-40\right)\left(44-50\right)$$

Subtract 44 from 30 to get -14.

$$\left(45-x\right)\left(-14\right)=\left(x-40\right)\left(44-50\right)$$

Use the distributive property to multiply 45-x by -14.

$$-630+14x=\left(x-40\right)\left(44-50\right)$$

Subtract 50 from 44 to get -6.

$$-630+14x=\left(x-40\right)\left(-6\right)$$

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

$$-630+14x=-6x+240$$

Add 6x to both sides.

$$-630+14x+6x=240$$

Combine 14x and 6x to get 20x.

$$-630+20x=240$$

Add 630 to both sides.

$$20x=240+630$$

Add 240 and 630 to get 870.

$$20x=870$$

Divide both sides by 20.

$$x=\frac{870}{20}$$

Reduce the fraction \frac{870}{20} to lowest terms by extracting and canceling out 10.

$$x=\frac{87}{2}$$