Examples of writing inequalities from number line graphs (8th grade math)

📚 Quick Study Guide

• 🔢 An inequality compares two values, showing if one is less than, greater than, less than or equal to, or greater than or equal to another.
• 📈 A number line visually represents inequalities. An open circle indicates values *not* included in the solution ( $<$ or $>$ ), while a closed circle indicates values *included* ($\leq$ or $\geq$).
• ➡️ The direction of the arrow on the number line shows the range of values that satisfy the inequality. To the right means greater than, to the left means less than.
• ✍️ To write an inequality, identify the number on the number line, whether the circle is open or closed, and the direction of the arrow. For example, a closed circle at 3 with an arrow to the right is $x \geq 3$.
• 💡 Remember that when multiplying or dividing both sides of an inequality by a negative number, you must flip the inequality sign!

Practice Quiz

1. What inequality is represented by an open circle on -2 with an arrow pointing to the right?
   1. $x < -2$
   2. $x \leq -2$
   3. $x > -2$
   4. $x \geq -2$
2. Which inequality is shown by a closed circle on 5 with an arrow pointing to the left?
   1. $x > 5$
   2. $x \geq 5$
   3. $x < 5$
   4. $x \leq 5$
3. The graph shows an open circle at 0 with an arrow extending to the left. Which inequality does it represent?
   1. $x > 0$
   2. $x < 0$
   3. $x \geq 0$
   4. $x \leq 0$
4. What inequality corresponds to a closed circle on -1 with an arrow going to the right?
   1. $x < -1$
   2. $x \leq -1$
   3. $x > -1$
   4. $x \geq -1$
5. Which of the following inequalities matches a number line with a closed circle at 2 and shading to the left?
   1. $x > 2$
   2. $x < 2$
   3. $x \geq 2$
   4. $x \leq 2$
6. A number line has an open circle at -4 and an arrow pointing to the right. What inequality does it represent?
   1. $x \leq -4$
   2. $x < -4$
   3. $x \geq -4$
   4. $x > -4$
7. What inequality is represented by the number line with a closed circle on 3 and an arrow pointing left?
   1. $x > 3$
   2. $x < 3$
   3. $x \geq 3$
   4. $x \leq 3$