Solve 2(x-1)-3(x+2)<6(1+x)

$$2 ( x - 1 ) - 3 ( x + 2 ) < 6 ( 1 + x )$$

Solve for x

$$x>-2$$

Solution Steps

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

$$2x-2-3\left(x+2\right)<6\left(1+x\right)$$

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

$$2x-2-3x-6<6\left(1+x\right)$$

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

$$-x-2-6<6\left(1+x\right)$$

Subtract 6 from -2 to get -8.

$$-x-8<6\left(1+x\right)$$

Use the distributive property to multiply 6 by 1+x.

$$-x-8<6+6x$$

Subtract 6x from both sides.

$$-x-8-6x<6$$

Combine -x and -6x to get -7x.

$$-7x-8<6$$

Add 8 to both sides.

$$-7x<6+8$$

Add 6 and 8 to get 14.

$$-7x<14$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>\frac{14}{-7}$$

Divide 14 by -7 to get -2.

$$x>-2$$