Solve the Inequality for y y+y/2>3

$y + \frac{y}{2} > 3$

Step 1

Simplify $y + \frac{y}{2}$ .

To write $y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y \cdot \frac{2}{2} + \frac{y}{2} > 3$

Simplify terms.

Combine $y$ and $\frac{2}{2}$ .

$\frac{y \cdot 2}{2} + \frac{y}{2} > 3$

Combine the numerators over the common denominator.

$\frac{y \cdot 2 + y}{2} > 3$

Simplify the numerator.

Move $2$ to the left of $y$ .

$\frac{2 \cdot y + y}{2} > 3$

Add $2 y$ and $y$ .

$\frac{3 y}{2} > 3$

Step 2

Multiply both sides by $2$ .

$\frac{3 y}{2} \cdot 2 > 3 \cdot 2$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 y}{2} \cdot 2 > 3 \cdot 2$

Rewrite the expression.

$3 y > 3 \cdot 2$

Simplify the right side.

Multiply $3$ by $2$ .

$3 y > 6$

Step 4

Divide each term in $3 y > 6$ by $3$ and simplify.

Divide each term in $3 y > 6$ by $3$ .

$\frac{3 y}{3} > \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{6}{3}$

Divide $y$ by $1$ .

$y > \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$y > 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y > 2$

Interval Notation:

$(2, \infty)$

Solve the Inequality for y y+y/2>3

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