Solve 2(x+7)<3(x+4)

$$2(x+7) < 3(x+4)$$

Solve for x

$$x>2$$

Solution Steps

Use the distributive property to multiply 2 by x+7.

$$2x+14<3\left(x+4\right)$$

Use the distributive property to multiply 3 by x+4.

$$2x+14<3x+12$$

Subtract 3x from both sides.

$$2x+14-3x<12$$

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

$$-x+14<12$$

Subtract 14 from both sides.

$$-x<12-14$$

Subtract 14 from 12 to get -2.

$$-x<-2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x>2$$