How to solve (x-1)/(2) > x+1

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-1)/(2) > x+1 | Equatix

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

$x<-3$

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

$$x-1>2x+2$$

Subtract $2x$ from both sides.

$$x-1-2x>2$$

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

$$-x-1>2$$

Add $1$ to both sides.

$$-x>2+1$$

Add $2$ and $1$ to get $3$.

$$-x>3$$

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

$$x<-3$$