Solve x-29/1970+x-27/1972+x-25/1974+x-23/1976+frac{x-1970}{29}+frac{x-1972}{27}+frac{x-1974}{25}+frac{x-1976}{23}-8=0

$$\frac { x - 29 } { 1970 } + \frac { x - 27 } { 1972 } + \frac { x - 25 } { 1974 } + \frac { x - 23 } { 1976 } + \frac { x - 1970 } { 29 } + \frac { x - 1972 } { 27 } + \frac { x - 1974 } { 25 } + \frac { x - 1976 } { 23 } - 8 = 0$$

Solve for x

$$x=1999$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 980229102816600, the least common multiple of 1970,1972,1974,1976,29,27,25,23.

$$497578224780\left(x-29\right)[phone]\left(x-27\right)[phone]\left(x-25\right)[phone]\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 497578224780 by x-29.

$$497578224780x-14429768518620+497073581550\left(x-27\right)[phone]\left(x-25\right)[phone]\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 497073581550 by x-27.

$$497578224780x-14429768518620+497073581550x-13420986701850+496569960900\left(x-25\right)[phone]\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Combine 497578224780x and 497073581550x to get 994651806330x.

$$994651806330x-14429768518620-13420986701850+496569960900\left(x-25\right)[phone]\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Subtract 13420986701850 from -14429768518620 to get -27850755220470.

$$994651806330x-27850755220470+496569960900\left(x-25\right)[phone]\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 496569960900 by x-25.

$$994651806330x-27850755220470+496569960900x-12414249022500+496067359725\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Combine 994651806330x and 496569960900x to get 1491221767230x.

$$1491221767230x-27850755220470-12414249022500+496067359725\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Subtract 12414249022500 from -27850755220470 to get -40265004242970.

$$1491221767230x-40265004242970+496067359725\left(x-23\right)[phone]\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 496067359725 by x-23.

$$1491221767230x-40265004242970+496067359725x-11409549273675+33801003545400\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Combine 1491221767230x and 496067359725x to get 1987289126955x.

$$1987289126955x-40265004242970-11409549273675+33801003545400\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Subtract 11409549273675 from -40265004242970 to get -51674553516645.

$$1987289126955x-51674553516645+33801003545400\left(x-1970\right)[phone]\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 33801003545400 by x-1970.

$$1987289126955x-51674553516645+33801003545400x-66587976984438000+36304781585800\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Combine 1987289126955x and 33801003545400x to get 35788292672355x.

$$35788292672355x-51674553516645-66587976984438000+36304781585800\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Subtract 66587976984438000 from -51674553516645 to get -66639651537954645.

$$35788292672355x-66639651537954645+36304781585800\left(x-1972\right)[phone]\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 36304781585800 by x-1972.

$$35788292672355x-66639651537954645+36304781585800x-71593029287197600+39209164112664\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Combine 35788292672355x and 36304781585800x to get 72093074258155x.

$$72093074258155x-66639651537954645-71593029287197600+39209164112664\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Subtract 71593029287197600 from -66639651537954645 to get -138232680825152245.

$$72093074258155x-138232680825152245+39209164112664\left(x-1974\right)[phone]\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 39209164112664 by x-1974.

$$72093074258155x-138232680825152245+39209164112664x-77398889958398736+42618656644200\left(x-1976\right)-7841832822532800=0$$

Combine 72093074258155x and 39209164112664x to get 111302238370819x.

$$111302238370819x-138232680825152245-77398889958398736+42618656644200\left(x-1976\right)-7841832822532800=0$$

Subtract 77398889958398736 from -138232680825152245 to get -215631570783550981.

$$111302238370819x-215631570783550981+42618656644200\left(x-1976\right)-7841832822532800=0$$

Use the distributive property to multiply 42618656644200 by x-1976.

$$111302238370819x-215631570783550981+42618656644200x-84214465528939200-7841832822532800=0$$

Combine 111302238370819x and 42618656644200x to get 153920895015019x.

$$153920895015019x-215631570783550981-84214465528939200-7841832822532800=0$$

Subtract 84214465528939200 from -215631570783550981 to get -299846036312490181.

$$153920895015019x-299846036312490181-7841832822532800=0$$

Subtract 7841832822532800 from -299846036312490181 to get -307687869135022981.

$$153920895015019x-307687869135022981=0$$

Add 307687869135022981 to both sides. Anything plus zero gives itself.

$$153920895015019x=307687869135022981$$

Divide both sides by 153920895015019.

$$x=\frac{307687869135022981}{153920895015019}$$

Divide 307687869135022981 by 153920895015019 to get 1999.

$$x=1999$$