Graphing Inequalities Worksheet Generator
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Pick a worksheet type and difficulty. You get number lines with open and closed circles, an answer key with the worked steps, and a new set every time you press the button.
Graphing Inequalities on a Number Line
Use an open circle for < and >. Use a filled-in circle for ≤ and ≥.
Graph the solution: x ≤ −5
Graph the solution: x ≤ −6
Graph the solution: x > −4
Graph the solution: x < 2
Graph the solution: x > 1
Graph the solution: x ≥ −6
Graphing Inequalities on a Number Line — Answer Key
x ≤ −5
x ≤ −6
x > −4
x < 2
x > 1
x ≥ −6
Quick check: try a few questions online
Which inequality means “x is at least 5”?
Correct answer: x ≥ 5. “At least” means 5 or more, so 5 is allowed. That is x ≥ 5. The graph has a filled-in circle at 5 and shading to the right.
Solve: −5x > 10
Correct answer: x < −2. Divide both sides by −5. Dividing by a negative number flips the inequality sign, so > becomes <, and 10 ÷ (−5) = −2. The answer is x < −2.
Which circle do you draw at 6 to graph x < 6?
Correct answer: An open circle. Strict inequalities (< and >) do not include the endpoint, so the circle is open. Use a filled-in circle only for ≤ and ≥.
Pick an answer for each question.
About this tool
Graphing an inequality asks students to connect three things: a symbol, a circle and a direction. Open or closed? Left or right? A short, well-chosen set of practice problems is the fastest way to make those choices automatic.
This generator makes five kinds of practice. Students can graph a given inequality, including statements written in words such as “x is at least 3”. They can read a graph and write the inequality it shows. They can solve a one-step or two-step inequality and graph the answer. And they can handle compound inequalities that use “and” or “or”.
For the solving problems, the key shows each step and flags the moment the inequality sign must flip, which happens when you multiply or divide by a negative number. Every answer is checked two ways: by testing the original inequality against the solution on a range of values, and by testing the drawn graph against the same values.
How to use it
- Choose the worksheet type. Graph the inequality is a good starting point. Mixed practice gives one of each type.
- For solve-and-graph sheets, pick easier for one-step problems, or harder for two-step problems with negative coefficients.
- Turn on word phrases to practice translating “at most”, “no less than” and similar wording into symbols.
- Press New worksheet for a fresh set, and print. Use the answer key to check graphs and worked steps.
Open or closed?
The symbols < and > are strict. They do not include the number at the endpoint, so the circle is open. The symbols ≤ and ≥ include the endpoint, so the circle is filled in. A quick way to remember it: a line under the symbol means the number is allowed in.
When the sign flips
If you multiply or divide both sides of an inequality by a negative number, reverse the inequality sign. For example, −2x > 8 becomes x < −4. Test it: pick x = −5. Then −2 × −5 = 10, and 10 is greater than 8, so x = −5 works.
Common questions
What grade is graphing inequalities for?
One-variable inequalities on a number line start in grade 6 and are extended in grade 7 with two-step problems. Compound inequalities appear in Algebra 1.
How do I graph an inequality on a number line?
Find the number in the inequality, draw an open circle for less than or greater than, or a filled-in circle for less than or equal to or greater than or equal to. Shade toward the numbers that make the inequality true.
Why does the inequality sign flip?
Multiplying or dividing by a negative number reverses the order of numbers. For example, 2 is greater than 1, but −2 is less than −1. The sign has to flip to keep the statement true.
Does the key show the steps?
Yes. For solve-and-graph problems, the key lists each step and calls out when the sign flips.
Can I include compound inequalities?
Yes. Choose Compound inequalities for problems that combine two conditions, such as x is greater than negative 2 and at most 5, or x is less than negative 1 or at least 3.
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