Example Card: Solving for y and Reversing the Inequality

What happens when 'y' is negative? A simple flip of a sign changes everything. This illustrates the key idea of how to deal with inequality when multiplying or dividing by a negative number.

Example Problem Graph the inequality $6x 2y < 8$.

Step by Step 1. To graph this inequality, we must first solve for $y$. Start with the given inequality. $$ 6x 2y < 8 $$ 2. Subtract $6x$ from both sides of the inequality. $$ 2y < 6x 8 $$ 3. Now, divide all three terms by $ 2$. Remember, when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol . $$ \frac{ 2y}{ 2} \frac{ 6x}{ 2} \frac{8}{ 2} $$ 4. Simplify the expression to get the inequality in slope intercept form. $$ y 3x + 4 $$ 5. Now we can graph the boundary line $y = 3x + 4$. We use a dashed line because the inequality symbol is $ $. Then we shade the region above the line, as indicated by the 'greater than' symbol.