Solve x-5/100+x-4/100+x-3/102=x-100/5+frac{x-101}{4}+frac{x-102}{3}

$$\frac{ x-5 }{ 100 } + \frac{ x-4 }{ 100 } + \frac{ x-3 }{ 102 } = \frac{ x-100 }{ 5 } + \frac{ x-101 }{ 4 } + \frac{ x-102 }{ 3 }$$

Solve for x

$$x = \frac{134522}{1281} = 105\frac{17}{1281} \approx 105.013270882$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5100, the least common multiple of 100,102,5,4,3.

$$51\left(x-5\right)+51\left(x-4\right)+50\left(x-3\right)=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Use the distributive property to multiply 51 by x-5.

$$51x-255+51\left(x-4\right)+50\left(x-3\right)=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Use the distributive property to multiply 51 by x-4.

$$51x-255+51x-204+50\left(x-3\right)=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Combine 51x and 51x to get 102x.

$$102x-255-204+50\left(x-3\right)=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Subtract 204 from -255 to get -459.

$$102x-459+50\left(x-3\right)=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Use the distributive property to multiply 50 by x-3.

$$102x-459+50x-150=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Combine 102x and 50x to get 152x.

$$152x-459-150=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Subtract 150 from -459 to get -609.

$$152x-609=1020\left(x-100\right)+1275\left(x-101\right)+1700\left(x-102\right)$$

Use the distributive property to multiply 1020 by x-100.

$$152x-609=1020x-102000+1275\left(x-101\right)+1700\left(x-102\right)$$

Use the distributive property to multiply 1275 by x-101.

$$152x-609=1020x-102000+1275x-128775+1700\left(x-102\right)$$

Combine 1020x and 1275x to get 2295x.

$$152x-609=2295x-102000-128775+1700\left(x-102\right)$$

Subtract 128775 from -102000 to get -230775.

$$152x-609=2295x-230775+1700\left(x-102\right)$$

Use the distributive property to multiply 1700 by x-102.

$$152x-609=2295x-230775+1700x-173400$$

Combine 2295x and 1700x to get 3995x.

$$152x-609=3995x-230775-173400$$

Subtract 173400 from -230775 to get -404175.

$$152x-609=3995x-404175$$

Subtract 3995x from both sides.

$$152x-609-3995x=-404175$$

Combine 152x and -3995x to get -3843x.

$$-3843x-609=-404175$$

Add 609 to both sides.

$$-3843x=-404175+609$$

Add -404175 and 609 to get -403566.

$$-3843x=-403566$$

Divide both sides by -3843.

$$x=\frac{-403566}{-3843}$$

Reduce the fraction \frac{-403566}{-3843} to lowest terms by extracting and canceling out -3.

$$x=\frac{134522}{1281}$$