A focused Grade 7 learning session for Graphing Solutions to Inequalities on a Number Line using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving graphing solutions to inequalities on a number line.
Graphing Solutions to Inequalities on a Number Line is part of Grade 7 Equations and Inequalities. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of graphing solutions to inequalities on a number line using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Graphing Solutions to Inequalities on a Number Line, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving graphing solutions to inequalities on a number line.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which number line represents the inequality \(x>-2\)?
Answer A: Open circle at \(-2\) pointing right
\(x>-2\) means strictly greater than (does not include) \(-2\), so use an open circle at \(-2\) and an arrow pointing right toward larger values.
Which number line represents the inequality \(x \leq 3\)?
Answer B: Closed circle at \(3\) pointing left
\(x \leq 3\) means less than or equal to \(3\) (includes 3), so use a closed circle at the boundary \(3\) and an arrow pointing left toward smaller values.
Which inequality is represented by the number line below?
Answer B: \(x > 0\)
An open circle at \(0\) with an arrow pointing right indicates all values greater than \(0\), which is \(x > 0\).
Which inequality is represented by the number line below?
Answer A: \(x \leq -1\)
A closed circle at \(-1\) with an arrow pointing left indicates all values less than or equal to \(-1\), which is \(x \leq -1\).
Identify the number line that correctly represents \(x < 5\).
Answer A: Open circle at \(5\) pointing left
\(x < 5\) uses an open circle (excludes \(5\)) and an arrow pointing left (toward smaller values less than \(5\)).
Which number line represents the inequality \(x \geq -3\)?
Answer C: Closed circle at \(-3\) pointing right
\(x \geq -3\) means greater than or equal to \(-3\) (includes \(-3\)), so use a closed circle at the boundary \(-3\) and an arrow pointing right.
What inequality does this number line represent?
Answer B: \(x < 2\)
An open circle at \(2\) with an arrow pointing left shows all values strictly less than \(2\), which is \(x < 2\).
Which number line represents the inequality \(x > -5\)?
Answer B: Open circle at \(-5\) pointing right
\(x > -5\) means strictly greater than \(-5\), so an open circle at \(-5\) with an arrow pointing right.
Which inequality is shown on this number line?
Answer C: \(x \geq 4\)
A closed circle at \(4\) with a right-pointing arrow indicates \(x \geq 4\) (greater than or equal to \(4\)).
A student writes the inequality \(x \leq -2\) but graphs it with an open circle instead of a closed circle at \(-2\). What value is incorrectly excluded from the solution set?
Answer B: The value \(-2\) itself
The inequality \(x \leq -2\) includes the boundary value \(-2\). Using an open circle instead of a closed circle removes \(-2\) from the solution set, changing it to \(x < -2\).
Choose the correct number line for the inequality \(n < -4\).
Answer A: Open circle at \(-4\) pointing left
\(n < -4\) uses an open circle (strict inequality) and points left toward smaller numbers.
