Testinar Grade 7 math

Graphing Solutions to Inequalities on a Number Line

Students will build Grade 7 mastery of graphing solutions to inequalities on a number line using models, equations, and test-style reasoning.

CH05-06 Equations and Inequalities

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which number line represents the inequality \(x>-2\)?
1. Open circle at \(-2\) pointing right
2. Closed circle at \(-2\) pointing right
3. Open circle at \(-2\) pointing left
4. Open circle at \(0\) pointing right
Which number line represents the inequality \(x \leq 3\)?
1. Open circle at \(3\) pointing left
2. Closed circle at \(3\) pointing left
3. Open circle at \(3\) pointing right
4. Closed circle at \(0\) pointing left
Which inequality is represented by the number line below?
1. \(x < 0\)
2. \(x > 0\)
3. \(x \leq 0\)
4. \(x \geq 0\)
Which inequality is represented by the number line below?
1. \(x \leq -1\)
2. \(x < -1\)
3. \(x \geq -1\)
4. \(x > -1\)
Identify the number line that correctly represents \(x < 5\).
1. Open circle at \(5\) pointing left
2. Closed circle at \(5\) pointing left
3. Open circle at \(5\) pointing right
4. Open circle at \(4\) pointing left
Which number line represents the inequality \(x \geq -3\)?
1. Open circle at \(-3\) pointing right
2. Closed circle at \(-3\) pointing left
3. Closed circle at \(-3\) pointing right
4. Open circle at \(-4\) pointing right
What inequality does this number line represent?
1. \(x > 2\)
2. \(x < 2\)
3. \(x \leq 2\)
4. \(x \geq 2\)
Which inequality is shown on this number line?
1. \(x < 4\)
2. \(x > 4\)
3. \(x \geq 4\)
4. \(x \leq 4\)

Teacher and parent reference

Answer key and explanations

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.
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.
B. \(x > 0\)
An open circle at \(0\) with an arrow pointing right indicates all values greater than \(0\), which is \(x > 0\).
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 \(x \leq -1\).
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 \(5\)).
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.
B. \(x < 2\)
An open circle at \(2\) with an arrow pointing left shows all values strictly less than \(2\), which is \(x < 2\).
C. \(x \geq 4\)
A closed circle at \(4\) with a right-pointing arrow indicates \(x \geq 4\) (greater than or equal to \(4\)).