Solve for x 3(x-2)<2(x+9)

$3 (x - 2) < 2 (x + 9)$

Simplify $3 (x - 2)$ .

Start simplifying.

$0 + 0 + 3 (x - 2) < 2 (x + 9)$

Simplify by adding zeros.

$3 (x - 2) < 2 (x + 9)$

Apply the distributive property.

$3 x + 3 \cdot - 2 < 2 (x + 9)$

Multiply $3$ by $- 2$ .

$3 x - 6 < 2 (x + 9)$

Simplify $2 (x + 9)$ .

Apply the distributive property.

$3 x - 6 < 2 x + 2 \cdot 9$

Multiply $2$ by $9$ .

$3 x - 6 < 2 x + 18$

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

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

$3 x - 6 - 2 x < 18$

Subtract $2 x$ from $3 x$ .

$x - 6 < 18$

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

Add $6$ to both sides of the inequality.

$x < 18 + 6$

Add $18$ and $6$ .

$x < 24$

The result can be shown in multiple forms.

Inequality Form:

$x < 24$

Interval Notation:

$(- \infty, 24)$