Solve the Inequality for x y>=1/2x-3

$y \geq \frac{1}{2} x - 3$

Step 1

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

$\frac{1}{2} x - 3 \leq y$

Step 2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - 3 \leq y$

Step 3

Add $3$ to both sides of the inequality.

$\frac{x}{2} \leq y + 3$

Step 4

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 \leq (y + 3) \cdot 2$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 \leq (y + 3) \cdot 2$

Rewrite the expression.

$x \leq (y + 3) \cdot 2$

Simplify the right side.

Simplify $(y + 3) \cdot 2$ .

Apply the distributive property.

$x \leq y \cdot 2 + 3 \cdot 2$

Simplify the expression.

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

$x \leq 2 \cdot y + 3 \cdot 2$

Multiply $3$ by $2$ .

$x \leq 2 y + 6$