Solve x+2/2+x+4/3=x+6/4+x+8/5

$$\frac { x + 2 } { 2 } + \frac { x + 4 } { 3 } = \frac { x + 6 } { 4 } + \frac { x + 8 } { 5 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 2,3,4,5.

$$30\left(x+2\right)+20\left(x+4\right)=15\left(x+6\right)+12\left(x+8\right)$$

Use the distributive property to multiply 30 by x+2.

$$30x+60+20\left(x+4\right)=15\left(x+6\right)+12\left(x+8\right)$$

Use the distributive property to multiply 20 by x+4.

$$30x+60+20x+80=15\left(x+6\right)+12\left(x+8\right)$$

Combine 30x and 20x to get 50x.

$$50x+60+80=15\left(x+6\right)+12\left(x+8\right)$$

Add 60 and 80 to get 140.

$$50x+140=15\left(x+6\right)+12\left(x+8\right)$$

Use the distributive property to multiply 15 by x+6.

$$50x+140=15x+90+12\left(x+8\right)$$

Use the distributive property to multiply 12 by x+8.

$$50x+140=15x+90+12x+96$$

Combine 15x and 12x to get 27x.

$$50x+140=27x+90+96$$

Add 90 and 96 to get 186.

$$50x+140=27x+186$$

Subtract 27x from both sides.

$$50x+140-27x=186$$

Combine 50x and -27x to get 23x.

$$23x+140=186$$

Subtract 140 from both sides.

$$23x=186-140$$

Subtract 140 from 186 to get 46.

$$23x=46$$

Divide both sides by 23.

$$x=\frac{46}{23}$$

Divide 46 by 23 to get 2.

$$x=2$$