Solve the Inequality for x 3<x/2+1

$3 < \frac{x}{2} + 1$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$\frac{x}{2} + 1 > 3$

Step 2

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

Subtract $1$ from both sides of the inequality.

$\frac{x}{2} > 3 - 1$

Subtract $1$ from $3$ .

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

Step 3

Multiply both sides by $2$ .

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

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x > 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$x > 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 4$

Interval Notation:

$(4, \infty)$