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

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

Solve for x

$$x>-\frac{5}{2}$$

Solution Steps

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

$$3x-12<7x-2$$

Subtract 7x from both sides.

$$3x-12-7x<-2$$

Combine 3x and -7x to get -4x.

$$-4x-12<-2$$

Add 12 to both sides.

$$-4x<-2+12$$

Add -2 and 12 to get 10.

$$-4x<10$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>\frac{10}{-4}$$

Reduce the fraction \frac{10}{-4} to lowest terms by extracting and canceling out 2.

$$x>-\frac{5}{2}$$