Solve 2(2x+3)+2(x+2)=2x+3+2x+3+x+2+x+2

$$2(2x+3)+2(x+2)=2x+3+2x+3+x+2+x+2$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 2 by 2x+3.

$$4x+6+2\left(x+2\right)=2x+3+2x+3+x+2+x+2$$

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

$$4x+6+2x+4=2x+3+2x+3+x+2+x+2$$

Combine 4x and 2x to get 6x.

$$6x+6+4=2x+3+2x+3+x+2+x+2$$

Add 6 and 4 to get 10.

$$6x+10=2x+3+2x+3+x+2+x+2$$

Combine 2x and 2x to get 4x.

$$6x+10=4x+3+3+x+2+x+2$$

Add 3 and 3 to get 6.

$$6x+10=4x+6+x+2+x+2$$

Combine 4x and x to get 5x.

$$6x+10=5x+6+2+x+2$$

Add 6 and 2 to get 8.

$$6x+10=5x+8+x+2$$

Combine 5x and x to get 6x.

$$6x+10=6x+8+2$$

Add 8 and 2 to get 10.

$$6x+10=6x+10$$

Subtract 6x from both sides.

$$6x+10-6x=10$$

Combine 6x and -6x to get 0.

$$10=10$$

Compare 10 and 10.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 2 by 2x+3.

$$4x+6+2\left(x+2\right)=2x+3+2x+3+x+2+x+2$$

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

$$4x+6+2x+4=2x+3+2x+3+x+2+x+2$$

Combine 4x and 2x to get 6x.

$$6x+6+4=2x+3+2x+3+x+2+x+2$$

Add 6 and 4 to get 10.

$$6x+10=2x+3+2x+3+x+2+x+2$$

Combine 2x and 2x to get 4x.

$$6x+10=4x+3+3+x+2+x+2$$

Add 3 and 3 to get 6.

$$6x+10=4x+6+x+2+x+2$$

Combine 4x and x to get 5x.

$$6x+10=5x+6+2+x+2$$

Add 6 and 2 to get 8.

$$6x+10=5x+8+x+2$$

Combine 5x and x to get 6x.

$$6x+10=6x+8+2$$

Add 8 and 2 to get 10.

$$6x+10=6x+10$$

Subtract 6x from both sides.

$$6x+10-6x=10$$

Combine 6x and -6x to get 0.

$$10=10$$

Compare 10 and 10.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$