Solve 4-3(x-2)geq-x-2(x+3)

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

Solve for x

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

Solution Steps

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

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

Add 4 and 6 to get 10.

$$10-3x\geq -x-2\left(x+3\right)$$

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

$$10-3x\geq -x-2x-6$$

Add x to both sides.

$$10-3x+x\geq -2x-6$$

Combine -3x and x to get -2x.

$$10-2x\geq -2x-6$$

Add 2x to both sides.

$$10-2x+2x\geq -6$$

Combine -2x and 2x to get 0.

$$10\geq -6$$

This is true for any x.

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