How to Graph Inequalities
Solve for the variable., Draw a number line., Draw a circle indicating the relative value., Draw an arrow indicating the included values.
Step-by-Step Guide
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Step 1: Solve for the variable.
To solve the inequality isolate the variable using the same algebraic methods you would use to solve an equation.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 3y+9>12{\displaystyle 3y+9>12}, isolate the variable by subtracting 9 from each side of the inequality, then dividing by 3:3y+9>12{\displaystyle 3y+9>12}3y+9−9>12−9{\displaystyle 3y+9-9>12-9}3y>3{\displaystyle 3y>3}3y3>33{\displaystyle {\frac {3y}{3}}>{\frac {3}{3}}}y>1{\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. -
Step 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 y>1{\displaystyle y>1}, make sure to include a point for 1 on the number line. , 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.For example, if y>1{\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. , If the variable is greater than the relative value, your arrow should point to the right, since the solution includes values greater than that number.
If the variable is less than the relative value, your arrow should point to the left, since the solution includes values less than that number.For example, for the solution y>1{\displaystyle y>1}, you would draw an arrow pointing to the right, since the solution includes values greater than
1. -
Step 3: Draw a circle indicating the relative value.
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Step 4: Draw an arrow indicating the included values.
Detailed Guide
To solve the inequality isolate the variable using the same algebraic methods you would use to solve an equation.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 3y+9>12{\displaystyle 3y+9>12}, isolate the variable by subtracting 9 from each side of the inequality, then dividing by 3:3y+9>12{\displaystyle 3y+9>12}3y+9−9>12−9{\displaystyle 3y+9-9>12-9}3y>3{\displaystyle 3y>3}3y3>33{\displaystyle {\frac {3y}{3}}>{\frac {3}{3}}}y>1{\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.
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 y>1{\displaystyle y>1}, make sure to include a point for 1 on the number line. , 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.For example, if y>1{\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. , If the variable is greater than the relative value, your arrow should point to the right, since the solution includes values greater than that number.
If the variable is less than the relative value, your arrow should point to the left, since the solution includes values less than that number.For example, for the solution y>1{\displaystyle y>1}, you would draw an arrow pointing to the right, since the solution includes values greater than
1.
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