Students will build Grade 6 mastery of graphing inequalities on a number line using models, equations, and test-style reasoning.
Which number line represents the inequality \(x>2\)?
Which inequality is represented by the number line?
Which number line shows the solution to \(x \le -1\)?
What inequality matches this number line?
Graph the inequality \(x \ge -2\) on a number line. Which description matches your graph?
Which inequality represents "all numbers less than \(5\)"?
Which number line shows \(x < -3\)?
Which number line represents \(x \le 0\)?
\(x>2\) means \(x\) is strictly greater than \(2\), so use an open circle (not including \(2\)) with the arrow pointing toward larger values.
A filled (closed) circle at \(3\) with an arrow pointing right indicates the number \(3\) is included and all numbers greater than \(3\) are solutions.
\(x \le -1\) means \(x\) equals \(-1\) or is less than \(-1\). A closed circle (filled) includes \(-1\), and the arrow points left (toward smaller values).
An open circle at \(6\) means \(6\) is not included. The arrow points left toward smaller values, so the inequality is \(x < 6\).
\(x \ge -2\) includes \(-2\) (closed circle) and all numbers greater than \(-2\) (arrow points right).
"Less than" does not include the boundary value, so we use the strict inequality \(x < 5\) (not \(\le\)).
\(x < -3\) means \(-3\) is not included (open circle) and we want all numbers less than \(-3\) (arrow pointing left).
\(x \le 0\) includes \(0\) (closed circle) and all numbers less than \(0\) (arrow points left).
