Solve 3left(1-3xright)<12left(2+xright)

$$3 \left( 1-3x \right) < 12 \left( 2+x \right)$$

Solve for x

$$x>-1$$

Solution Steps

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

$$3-9x<12\left(2+x\right)$$

Use the distributive property to multiply 12 by 2+x.

$$3-9x<24+12x$$

Subtract 12x from both sides.

$$3-9x-12x<24$$

Combine -9x and -12x to get -21x.

$$3-21x<24$$

Subtract 3 from both sides.

$$-21x<24-3$$

Subtract 3 from 24 to get 21.

$$-21x<21$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$x>\frac{21}{-21}$$

Divide 21 by -21 to get -1.

$$x>-1$$