Solve 3(1-x)<12(2+x)

$$3(1-x) < 12(2+x)$$

Solve for x

$$x>-\frac{7}{5}$$

Solution Steps

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

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

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

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

Subtract 12x from both sides.

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

Combine -3x and -12x to get -15x.

$$3-15x<24$$

Subtract 3 from both sides.

$$-15x<24-3$$

Subtract 3 from 24 to get 21.

$$-15x<21$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x>\frac{21}{-15}$$

Reduce the fraction \frac{21}{-15} to lowest terms by extracting and canceling out 3.

$$x>-\frac{7}{5}$$