Representing Inequalities on a Number Line Flashcards

All 7 cards in this deck

On a number line, what does an open (unshaded) circle show?

That the end value is not included, i.e. the sign is $<$ or $>$.

On a number line, what does a closed (shaded) circle show?

That the end value is included, i.e. the sign is $\le$ or $\ge$.

What are the steps to show an inequality with one bound on a number line?

e.g. show $x < 4$

1. Draw the circle at the end value: circle at $4$.
2. Shade it only if the sign is $\le$ or $\ge$: leave it open.
3. Draw a line with an arrow in the direction of the solutions: arrow pointing left.

What are the steps to show a double inequality on a number line?

e.g. show $-3 \le y < 4$

1. Put a circle at each end value: circles at $-3$ and $4$.
2. Shade each circle only if that sign is $\le$ or $\ge$: closed at $-3$, open at $4$.
3. Join the circles with a line: line from $-3$ to $4$.

How do you write down the inequality shown on a number line?

e.g. open circle at $-1$ with an arrow pointing right

Read the end value, use $<$/$>$ for an open circle and $\le$/$\ge$ for a closed one, and match the sign to the arrow direction.

e.g. $x > -1$.

True or false? Circling the number $4$ on a number line is enough to show $x < 4$.

False. You also need the circle unshaded and a line with an arrow going left.

True or false? When you write down the inequality from a number line, an arrow pointing right means the sign is $>$ or $\ge$.

True. The solutions are the values greater than the circled number.