Solve x-3/2+x-5/3+x-2/5=1

$$\frac { x - 3 } { 2 } + \frac { x - 5 } { 3 } + \frac { x - 2 } { 5 } = 1$$

Solve for x

$$x = \frac{137}{31} = 4\frac{13}{31} \approx 4.419354839$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 2,3,5.

$$15\left(x-3\right)+10\left(x-5\right)+6\left(x-2\right)=30$$

Use the distributive property to multiply 15 by x-3.

$$15x-45+10\left(x-5\right)+6\left(x-2\right)=30$$

Use the distributive property to multiply 10 by x-5.

$$15x-45+10x-50+6\left(x-2\right)=30$$

Combine 15x and 10x to get 25x.

$$25x-45-50+6\left(x-2\right)=30$$

Subtract 50 from -45 to get -95.

$$25x-95+6\left(x-2\right)=30$$

Use the distributive property to multiply 6 by x-2.

$$25x-95+6x-12=30$$

Combine 25x and 6x to get 31x.

$$31x-95-12=30$$

Subtract 12 from -95 to get -107.

$$31x-107=30$$

Add 107 to both sides.

$$31x=30+107$$

Add 30 and 107 to get 137.

$$31x=137$$

Divide both sides by 31.

$$x=\frac{137}{31}$$