Solve 29-x/21+27-x/23+25-x/25+23-x/27+frac{21-x}{29}=-5

$$\frac { 29 - x } { 21 } + \frac { 27 - x } { 23 } + \frac { 25 - x } { 25 } + \frac { 23 - x } { 27 } + \frac { 21 - x } { 29 } = - 5$$

Solve for x

$$x=50$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3151575, the least common multiple of 21,23,25,27,29.

$$150075\left(29-x\right)+137025\left(27-x\right)+126063\left(25-x\right)+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Use the distributive property to multiply 150075 by 29-x.

$$4352175-150075x+137025\left(27-x\right)+126063\left(25-x\right)+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Use the distributive property to multiply 137025 by 27-x.

$$4352175-150075x+3699675-137025x+126063\left(25-x\right)+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Add 4352175 and 3699675 to get 8051850.

$$8051850-150075x-137025x+126063\left(25-x\right)+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Combine -150075x and -137025x to get -287100x.

$$8051850-287100x+126063\left(25-x\right)+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Use the distributive property to multiply 126063 by 25-x.

$$8051850-287100x+3151575-126063x+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Add 8051850 and 3151575 to get 11203425.

$$11203425-287100x-126063x+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Combine -287100x and -126063x to get -413163x.

$$11203425-413163x+116725\left(23-x\right)+108675\left(21-x\right)=-15757875$$

Use the distributive property to multiply 116725 by 23-x.

$$11203425-413163x+2684675-116725x+108675\left(21-x\right)=-15757875$$

Add 11203425 and 2684675 to get 13888100.

$$13888100-413163x-116725x+108675\left(21-x\right)=-15757875$$

Combine -413163x and -116725x to get -529888x.

$$13888100-529888x+108675\left(21-x\right)=-15757875$$

Use the distributive property to multiply 108675 by 21-x.

$$13888100-529888x+2282175-108675x=-15757875$$

Add 13888100 and 2282175 to get 16170275.

$$16170275-529888x-108675x=-15757875$$

Combine -529888x and -108675x to get -638563x.

$$16170275-638563x=-15757875$$

Subtract 16170275 from both sides.

$$-638563x=-15757875-16170275$$

Subtract 16170275 from -15757875 to get -31928150.

$$-638563x=-31928150$$

Divide both sides by -638563.

$$x=\frac{-31928150}{-638563}$$

Divide -31928150 by -638563 to get 50.

$$x=50$$