Absolute Value Inequalities Graphing Quiz with Answers (Algebra 1)

📚 Quick Study Guide

🔢 Absolute Value Definition: The absolute value of a number is its distance from zero. It is always non-negative. 📏 Solving Absolute Value Equations: For $|x| = a$, where $a > 0$, then $x = a$ or $x = -a$. 🚧 Solving Absolute Value Inequalities ($<$ or $\leq$): For $|x| < a$, where $a > 0$, then $-a < x < a$. For $|x| \leq a$, where $a > 0$, then $-a \leq x \leq a$. ➕ Solving Absolute Value Inequalities ($>$ or $\geq$): For $|x| > a$, where $a > 0$, then $x < -a$ or $x > a$. For $|x| \geq a$, where $a > 0$, then $x \leq -a$ or $x \geq a$. 📈 Graphing on a Number Line: Use open circles for $<$ and $>$, and closed circles for $\leq$ and $\geq$. 💡 Key Tip: Isolate the absolute value expression before solving the inequality.

Practice Quiz

1. What is the solution to $|x| < 3$?
1. $x < 3$
2. $x > -3$
3. $-3 < x < 3$
4. $x < -3$ or $x > 3$
2. What is the solution to $|x| \geq 5$?
1. $-5 \leq x \leq 5$
2. $x \leq -5$ or $x \geq 5$
3. $x \geq 5$
4. $x \leq 5$
3. Which graph represents the solution to $|x - 2| < 4$?
1. A number line with an open interval between -2 and 6.
2. A number line with a closed interval between -2 and 6.
3. A number line with open intervals to the left of -2 and to the right of 6.
4. A number line with closed intervals to the left of -2 and to the right of 6.
4. Solve for $x$: $|2x + 1| \leq 7$
1. $x \leq 3$
2. $-4 \leq x \leq 3$
3. $x \leq -4$ or $x \geq 3$
4. $-3 \leq x \leq 4$
5. What inequality is represented by the graph with a closed interval between -1 and 5?
1. $|x - 2| \leq 3$
2. $|x + 2| \leq 3$
3. $|x - 3| \leq 2$
4. $|x + 3| \leq 2$
6. Solve for $x$: $|3x - 6| > 9$
1. $x > 5$
2. $x < -1$
3. $-1 < x < 5$
4. $x < -1$ or $x > 5$
7. Which of the following is the correct graph for $|x + 4| \geq 2$?
1. A number line with a closed interval between -6 and -2.
2. A number line with open intervals to the left of -6 and to the right of -2.
3. A number line with closed intervals to the left of -6 and to the right of -2.
4. A number line with an open interval between -6 and -2.