How do you graph inequalities y
Answers
Solve for the variable. To solve the inequality isolate the variable using the same algebraic methods you would use to solve an equation.[1] Remember that when you multiply or divide by a negative number, you need to flip the inequality sign.
For example, if you are solving the inequality {\displaystyle 3y+9>12}, isolate the variable by subtracting 9 from each side of the inequality, then dividing by 3:
{\displaystyle 3y+9>12}
{\displaystyle 3y+9-9>12-9}
{\displaystyle 3y>3}
{\displaystyle {\frac {3y}{3}}>{\frac {3}{3}}}
{\displaystyle y>1}
Your inequality should only have one variable. If your inequality has two variables, it is more appropriate to graph it on a coordinate plane using another method.
Image titled Graph Inequalities Step 2
2
Draw a number line. Include the relative value on your number line (the value you found the variable to be less than, greater than, or equal to). Make the number line as long or short as required.
For example, if you found that {\displaystyle y>1}, make sure to include a point for 1 on the number line.
Image titled Graph Inequalities Step 3
3
Draw a circle indicating the relative value. If the value is less than ({\displaystyle <}) or greater than ({\displaystyle >}) this number, the circle should be open, since the solution does not include the value. If the value is less than or equal to ({\displaystyle \leq }), or greater than or equal to ({\displaystyle \geq }), the circle should be filled in, since the solution includes the value.[2]
For example, if {\displaystyle y>1}, you would draw a circle at 1 on the number line. You would not fill in the circle, since 1 is not included in the solution.