Solve x+3/2+x+4/3+x+5/4+x+6/5+frac{x+7}{6}=5

$$\frac { x + 3 } { 2 } + \frac { x + 4 } { 3 } + \frac { x + 5 } { 4 } + \frac { x + 6 } { 5 } + \frac { x + 7 } { 6 } = 5$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 2,3,4,5,6.

$$30\left(x+3\right)+20\left(x+4\right)+15\left(x+5\right)+12\left(x+6\right)+10\left(x+7\right)=300$$

Use the distributive property to multiply 30 by x+3.

$$30x+90+20\left(x+4\right)+15\left(x+5\right)+12\left(x+6\right)+10\left(x+7\right)=300$$

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

$$30x+90+20x+80+15\left(x+5\right)+12\left(x+6\right)+10\left(x+7\right)=300$$

Combine 30x and 20x to get 50x.

$$50x+90+80+15\left(x+5\right)+12\left(x+6\right)+10\left(x+7\right)=300$$

Add 90 and 80 to get 170.

$$50x+170+15\left(x+5\right)+12\left(x+6\right)+10\left(x+7\right)=300$$

Use the distributive property to multiply 15 by x+5.

$$50x+170+15x+75+12\left(x+6\right)+10\left(x+7\right)=300$$

Combine 50x and 15x to get 65x.

$$65x+170+75+12\left(x+6\right)+10\left(x+7\right)=300$$

Add 170 and 75 to get 245.

$$65x+245+12\left(x+6\right)+10\left(x+7\right)=300$$

Use the distributive property to multiply 12 by x+6.

$$65x+245+12x+72+10\left(x+7\right)=300$$

Combine 65x and 12x to get 77x.

$$77x+245+72+10\left(x+7\right)=300$$

Add 245 and 72 to get 317.

$$77x+317+10\left(x+7\right)=300$$

Use the distributive property to multiply 10 by x+7.

$$77x+317+10x+70=300$$

Combine 77x and 10x to get 87x.

$$87x+317+70=300$$

Add 317 and 70 to get 387.

$$87x+387=300$$

Subtract 387 from both sides.

$$87x=300-387$$

Subtract 387 from 300 to get -87.

$$87x=-87$$

Divide both sides by 87.

$$x=\frac{-87}{87}$$

Divide -87 by 87 to get -1.

$$x=-1$$