Solve the Inequality for x (3x)/2-2>7

$\frac{3 x}{2} - 2 > 7$

Step 1

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

Add $2$ to both sides of the inequality.

$\frac{3 x}{2} > 7 + 2$

Add $7$ and $2$ .

$\frac{3 x}{2} > 9$

Step 2

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 > 9 \cdot 2$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 > 9 \cdot 2$

Rewrite the expression.

$3 x > 9 \cdot 2$

Simplify the right side.

Multiply $9$ by $2$ .

$3 x > 18$

Step 4

Divide each term in $3 x > 18$ by $3$ and simplify.

Divide each term in $3 x > 18$ by $3$ .

$\frac{3 x}{3} > \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{18}{3}$

Divide $x$ by $1$ .

$x > \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$x > 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$