Solve the Inequality for x 3(x-3)<=2(x+2)

$3 (x - 3) \leq 2 (x + 2)$

Step 1

Simplify $3 (x - 3)$ .

Start simplifying.

$0 + 0 + 3 (x - 3) \leq 2 (x + 2)$

Simplify by adding zeros.

$3 (x - 3) \leq 2 (x + 2)$

Apply the distributive property.

$3 x + 3 \cdot - 3 \leq 2 (x + 2)$

Multiply $3$ by $- 3$ .

$3 x - 9 \leq 2 (x + 2)$

Step 2

Simplify $2 (x + 2)$ .

Apply the distributive property.

$3 x - 9 \leq 2 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$3 x - 9 \leq 2 x + 4$

Step 3

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

Subtract $2 x$ from both sides of the inequality.

$3 x - 9 - 2 x \leq 4$

Subtract $2 x$ from $3 x$ .

$x - 9 \leq 4$

Step 4

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

Add $9$ to both sides of the inequality.

$x \leq 4 + 9$

Add $4$ and $9$ .

$x \leq 13$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 13$

Interval Notation:

$(- \infty, 13]$