Solve 4(x+1)>2-3(2x+6)

$$4 ( x + 1 ) > 2 - 3 ( 2 x + 6 )$$

Solve for x

$$x>-2$$

Solution Steps

Use the distributive property to multiply 4 by x+1.

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

Use the distributive property to multiply -3 by 2x+6.

$$4x+4>2-6x-18$$

Subtract 18 from 2 to get -16.

$$4x+4>-16-6x$$

Add 6x to both sides.

$$4x+4+6x>-16$$

Combine 4x and 6x to get 10x.

$$10x+4>-16$$

Subtract 4 from both sides.

$$10x>-16-4$$

Subtract 4 from -16 to get -20.

$$10x>-20$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x>\frac{-20}{10}$$

Divide -20 by 10 to get -2.

$$x>-2$$