Solve the Inequality for x 9(2x+1)<9x-18

$9 (2 x + 1) < 9 x - 18$

Step 1

Simplify $9 (2 x + 1)$ .

Rewrite.

$0 + 0 + 9 (2 x + 1) < 9 x - 18$

Simplify by adding zeros.

$9 (2 x + 1) < 9 x - 18$

Apply the distributive property.

$9 (2 x) + 9 \cdot 1 < 9 x - 18$

Multiply.

Multiply $2$ by $9$ .

$18 x + 9 \cdot 1 < 9 x - 18$

Multiply $9$ by $1$ .

$18 x + 9 < 9 x - 18$

Step 2

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

Subtract $9 x$ from both sides of the inequality.

$18 x + 9 - 9 x < - 18$

Subtract $9 x$ from $18 x$ .

$9 x + 9 < - 18$

Step 3

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

Subtract $9$ from both sides of the inequality.

$9 x < - 18 - 9$

Subtract $9$ from $- 18$ .

$9 x < - 27$

Step 4

Divide each term in $9 x < - 27$ by $9$ and simplify.

Divide each term in $9 x < - 27$ by $9$ .

$\frac{9 x}{9} < \frac{- 27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} < \frac{- 27}{9}$

Divide $x$ by $1$ .

$x < \frac{- 27}{9}$

Simplify the right side.

Divide $- 27$ by $9$ .

$x < - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 3$

Interval Notation:

$(- \infty, - 3)$