Solve 3(x+1)+2(x+3)geq2x+3(x+3)

$$3 ( x + 1 ) + 2 ( x + 3 ) \geq 2 x + 3 ( x + 3 )$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 3 by x+1.

$$3x+3+2\left(x+3\right)\geq 2x+3\left(x+3\right)$$

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

$$3x+3+2x+6\geq 2x+3\left(x+3\right)$$

Combine 3x and 2x to get 5x.

$$5x+3+6\geq 2x+3\left(x+3\right)$$

Add 3 and 6 to get 9.

$$5x+9\geq 2x+3\left(x+3\right)$$

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

$$5x+9\geq 2x+3x+9$$

Combine 2x and 3x to get 5x.

$$5x+9\geq 5x+9$$

Subtract 5x from both sides.

$$5x+9-5x\geq 9$$

Combine 5x and -5x to get 0.

$$9\geq 9$$

This is true for any x.

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