Solve the Inequality for x 3x+2>-2(x-1)

$3 x + 2 > - 2 (x - 1)$

Step 1

Simplify $- 2 (x - 1)$ .

Rewrite.

$3 x + 2 > 0 + 0 - 2 (x - 1)$

Simplify by adding zeros.

$3 x + 2 > - 2 (x - 1)$

Apply the distributive property.

$3 x + 2 > - 2 x - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$3 x + 2 > - 2 x + 2$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Add $2 x$ to both sides of the inequality.

$3 x + 2 + 2 x > 2$

Add $3 x$ and $2 x$ .

$5 x + 2 > 2$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

Subtract $2$ from both sides of the inequality.

$5 x > 2 - 2$

Subtract $2$ from $2$ .

$5 x > 0$

Step 4

Divide each term in $5 x > 0$ by $5$ and simplify.

Divide each term in $5 x > 0$ by $5$ .

$\frac{5 x}{5} > \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{0}{5}$

Divide $x$ by $1$ .

$x > \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x > 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 0$

Interval Notation:

$(0, \infty)$