How to solve (2(x+2))/(3) < 2x

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 (2(x+2))/(3) < 2x | Equatix

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

$x>1$

Multiply both sides of the equation by $3$. Since $3$ is positive, the inequality direction remains the same.

$$2\left(x+2\right)<6x$$

Use the distributive property to multiply $2$ by $x+2$.

$$2x+4<6x$$

Subtract $6x$ from both sides.

$$2x+4-6x<0$$

Combine $2x$ and $-6x$ to get $-4x$.

$$-4x+4<0$$

Subtract $4$ from both sides. Anything subtracted from zero gives its negation.

$$-4x<-4$$

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

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

Divide $-4$ by $-4$ to get $1$.

$$x>1$$