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

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

Solve for x

$$x<-5$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x-1.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$x+2<\frac{1}{2}x-\frac{1}{2}$$

Subtract \frac{1}{2}x from both sides.

$$x+2-\frac{1}{2}x<-\frac{1}{2}$$

Combine x and -\frac{1}{2}x to get \frac{1}{2}x.

$$\frac{1}{2}x+2<-\frac{1}{2}$$

Subtract 2 from both sides.

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

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{2}x<-\frac{1}{2}-\frac{4}{2}$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x<\frac{-1-4}{2}$$

Subtract 4 from -1 to get -5.

$$\frac{1}{2}x<-\frac{5}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$x<-\frac{5}{2}\times 2$$

Cancel out 2 and 2.

$$x<-5$$