Real-World Examples of Contradiction Equations

📚 Quick Study Guide

• 🧐 A contradiction equation is an equation that is always false, regardless of the value of the variable.
• 🧮 When solving a contradiction equation, you'll often find that the variable cancels out, leaving you with a false statement.
• 📝 Examples of false statements include: $5 = 7$, $0 = 1$, or $-2 = 2$.
• 💡 The solution set for a contradiction equation is the empty set, denoted by $\emptyset$ or $\{ \}$.
• ➗ Common steps to identify a contradiction equation involve simplifying both sides of the equation and observing if a false statement arises.
• 📐 Remember to distribute, combine like terms, and isolate the variable when solving equations.
• 🧠 If you end up with a statement like $a = b$ where $a$ and $b$ are different numbers, you have a contradiction.

🧪 Practice Quiz

1. Which of the following equations is a contradiction equation?
   1. A. $x + 5 = x + 5$
   2. B. $2x + 3 = 2x - 1$
   3. C. $3x - 4 = 5$
   4. D. $x + 1 = 2$
2. What is the solution set for the equation $4(y - 2) = 4y + 8$?
   1. A. ${0}$
   2. B. All real numbers
   3. C. $\emptyset$
   4. D. ${-4}$
3. Identify the contradiction equation among the following:
   1. A. $5z + 2 = 7$
   2. B. $-3z = 0$
   3. C. $6z - 1 = 6z - 1$
   4. D. $2(z + 3) = 2z + 1$
4. Solve for $x$: $3(x + 1) - 5 = 3x - 2$
   1. A. $x = 0$
   2. B. $x = 1$
   3. C. All real numbers
   4. D. No solution
5. Which equation has no solution?
   1. A. $7w - 3 = 7w - 3$
   2. B. $w + 4 = 9$
   3. C. $2(w - 5) = 2w + 10$
   4. D. $5w = 0$
6. What type of equation is $-(v + 4) = -v + 6$?
   1. A. Identity
   2. B. Conditional
   3. C. Contradiction
   4. D. Linear
7. Determine the solution set for the equation: $8(u - 1) = 8u + 5$
   1. A. ${-13/8}$
   2. B. All real numbers
   3. C. $\emptyset$
   4. D. ${13/8}$