Solve the Inequality for x (3x)/2-6<9

$\frac{3 x}{2} - 6 < 9$

Step 1

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

Add $6$ to both sides of the inequality.

$\frac{3 x}{2} < 9 + 6$

Add $9$ and $6$ .

$\frac{3 x}{2} < 15$

Step 2

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 < 15 \cdot 2$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 < 15 \cdot 2$

Rewrite the expression.

$3 x < 15 \cdot 2$

Simplify the right side.

Multiply $15$ by $2$ .

$3 x < 30$

Step 4

Divide each term in $3 x < 30$ by $3$ and simplify.

Divide each term in $3 x < 30$ by $3$ .

$\frac{3 x}{3} < \frac{30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{30}{3}$

Divide $x$ by $1$ .

$x < \frac{30}{3}$

Simplify the right side.

Divide $30$ by $3$ .

$x < 10$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 10$

Interval Notation:

$(- \infty, 10)$