Solve x+x+1+x+2+x+3+x+4+x+5+x+6+x7=21

$$x+x+1+x+2+x+3+x+4+x+5+x+6+x7=21$$

Solve for x

$$x=-\frac{x_{7}}{7}$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$2x+1+x+2+x+3+x+4+x+5+x+6+x_{7}=21$$

Combine 2x and x to get 3x.

$$3x+1+2+x+3+x+4+x+5+x+6+x_{7}=21$$

Add 1 and 2 to get 3.

$$3x+3+x+3+x+4+x+5+x+6+x_{7}=21$$

Combine 3x and x to get 4x.

$$4x+3+3+x+4+x+5+x+6+x_{7}=21$$

Add 3 and 3 to get 6.

$$4x+6+x+4+x+5+x+6+x_{7}=21$$

Combine 4x and x to get 5x.

$$5x+6+4+x+5+x+6+x_{7}=21$$

Add 6 and 4 to get 10.

$$5x+10+x+5+x+6+x_{7}=21$$

Combine 5x and x to get 6x.

$$6x+10+5+x+6+x_{7}=21$$

Add 10 and 5 to get 15.

$$6x+15+x+6+x_{7}=21$$

Combine 6x and x to get 7x.

$$7x+15+6+x_{7}=21$$

Add 15 and 6 to get 21.

$$7x+21+x_{7}=21$$

Subtract 21 from both sides.

$$7x+x_{7}=21-21$$

Subtract 21 from 21 to get 0.

$$7x+x_{7}=0$$

Subtract x_{7} from both sides. Anything subtracted from zero gives its negation.

$$7x=-x_{7}$$

Divide both sides by 7.

$$\frac{7x}{7}=-\frac{x_{7}}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=-\frac{x_{7}}{7}$$

Solve for x_7

$$x_{7}=-7x$$

Solution Steps

Combine x and x to get 2x.

$$2x+1+x+2+x+3+x+4+x+5+x+6+x_{7}=21$$

Combine 2x and x to get 3x.

$$3x+1+2+x+3+x+4+x+5+x+6+x_{7}=21$$

Add 1 and 2 to get 3.

$$3x+3+x+3+x+4+x+5+x+6+x_{7}=21$$

Combine 3x and x to get 4x.

$$4x+3+3+x+4+x+5+x+6+x_{7}=21$$

Add 3 and 3 to get 6.

$$4x+6+x+4+x+5+x+6+x_{7}=21$$

Combine 4x and x to get 5x.

$$5x+6+4+x+5+x+6+x_{7}=21$$

Add 6 and 4 to get 10.

$$5x+10+x+5+x+6+x_{7}=21$$

Combine 5x and x to get 6x.

$$6x+10+5+x+6+x_{7}=21$$

Add 10 and 5 to get 15.

$$6x+15+x+6+x_{7}=21$$

Combine 6x and x to get 7x.

$$7x+15+6+x_{7}=21$$

Add 15 and 6 to get 21.

$$7x+21+x_{7}=21$$

Subtract 7x from both sides.

$$21+x_{7}=21-7x$$

Subtract 21 from both sides.

$$x_{7}=21-7x-21$$

Subtract 21 from 21 to get 0.

$$x_{7}=-7x$$