Step-by-step examples for identifying inequality solutions

📚 Quick Study Guide

• 🔢 Basic Inequality Symbols:
  • $>$: Greater than
  • $<$: Less than
  • $\geq$: Greater than or equal to
  • $\leq$: Less than or equal to
• ➗ Solving Inequalities: Treat them like equations, but if you multiply or divide by a negative number, flip the inequality sign.
• 📈 Graphing on a Number Line: Use open circles (o) for $<$ and $>$, and closed circles (•) for $\leq$ and $\geq$. Shade the region that satisfies the inequality.
• 💡 Interval Notation: A way to write solutions. For example, $x > 3$ is written as $(3, \infty)$.
• 📝 Compound Inequalities: Combine two inequalities with "and" or "or". Solve each separately and then combine the solutions.

Practice Quiz

1. What is the solution to the inequality $2x + 3 < 7$?
   1. $x < 2$
   2. $x > 2$
   3. $x < 5$
   4. $x > 5$
2. Solve for $x$: $-3x \geq 12$
   1. $x \geq -4$
   2. $x \leq -4$
   3. $x \geq 4$
   4. $x \leq 4$
3. Which graph represents the solution to $x > -1$?
   1. A number line with an open circle at -1 and shading to the left.
   2. A number line with a closed circle at -1 and shading to the left.
   3. A number line with an open circle at -1 and shading to the right.
   4. A number line with a closed circle at -1 and shading to the right.
4. What is the interval notation for $x \leq 5$?
   1. $(-\infty, 5)$
   2. $(-\infty, 5]$
   3. $(5, \infty)$
   4. $[5, \infty)$
5. Solve the compound inequality: $2 < x + 1 \leq 4$
   1. $1 < x \leq 3$
   2. $1 \leq x < 3$
   3. $3 < x \leq 5$
   4. $3 \leq x < 5$
6. Solve: $\frac{x}{2} - 1 > 3$
   1. $x > 4$
   2. $x < 4$
   3. $x > 8$
   4. $x < 8$
7. What is the solution to $|x| < 3$?
   1. $x < 3$
   2. $x > -3$
   3. $-3 < x < 3$
   4. $x < -3 \text{ or } x > 3$