Solve 2(x+1)geq4-(x+3)-3(2-x)

$$2 ( x + 1 ) \geq 4 - ( x + 3 ) - 3 ( 2 - x )$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 2 by x+1.

$$2x+2\geq 4-\left(x+3\right)-3\left(2-x\right)$$

To find the opposite of x+3, find the opposite of each term.

$$2x+2\geq 4-x-3-3\left(2-x\right)$$

Subtract 3 from 4 to get 1.

$$2x+2\geq 1-x-3\left(2-x\right)$$

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

$$2x+2\geq 1-x-6+3x$$

Subtract 6 from 1 to get -5.

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

Combine -x and 3x to get 2x.

$$2x+2\geq -5+2x$$

Subtract 2x from both sides.

$$2x+2-2x\geq -5$$

Combine 2x and -2x to get 0.

$$2\geq -5$$

This is true for any x.

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