Solve x-5<3x-6

$$x - 5 < 3 x - 6$$

Solve for x

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

Solution Steps

Subtract 3x from both sides.

$$x-5-3x<-6$$

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

$$-2x-5<-6$$

Add 5 to both sides.

$$-2x<-6+5$$

Add -6 and 5 to get -1.

$$-2x<-1$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

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

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

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