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

$$\frac { x + 1 } { 2 } + 2 < 3 ( x - 1 )$$

Solve for x

$$x>\frac{11}{5}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$x+1+4<6\left(x-1\right)$$

Add 1 and 4 to get 5.

$$x+5<6\left(x-1\right)$$

Use the distributive property to multiply 6 by x-1.

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

Subtract 6x from both sides.

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

Combine x and -6x to get -5x.

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

Subtract 5 from both sides.

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

Subtract 5 from -6 to get -11.

$$-5x<-11$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{11}{5}$$