Solved Examples: Evaluating Expressions by Substitution

📚 Quick Study Guide

• 🔢 Substitution: Replacing variables (like $x$, $y$, or $a$) with their given numerical values in an expression.
• ➕ Order of Operations (PEMDAS/BODMAS): Remember the correct sequence: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
• ✏️ Example: If $x = 3$ and the expression is $2x + 5$, substitute to get $2(3) + 5$.
• ➗ Simplify: Perform the arithmetic operations in the correct order. In the example above, $2(3) + 5 = 6 + 5 = 11$.
• ✅ Fractions and Decimals: Be careful when substituting with fractions or decimals. Ensure you perform the correct arithmetic operations.
• 💡 Tips: Always write down the substituted expression to avoid errors. Double-check your arithmetic.
• 📝 Complex Expressions: Break down complex expressions into smaller, manageable parts.

Practice Quiz

1. What is the value of the expression $3x + 2$ when $x = 4$?
   1. 10
   2. 14
   3. 20
   4. 24
2. Evaluate the expression $y^2 - 3y + 1$ when $y = 2$.
   1. -1
   2. -3
   3. 1
   4. 3
3. What is the value of $5a - 2b$ when $a = 3$ and $b = 1$?
   1. 11
   2. 13
   3. 17
   4. 19
4. If $p = -2$, what is the value of $p^3 + 4$?
   1. -12
   2. -4
   3. 4
   4. 12
5. Evaluate $\frac{x + 5}{2}$ when $x = -1$.
   1. 2
   2. 3
   3. 4
   4. 5
6. What is the value of $4(m - n)$ when $m = 7$ and $n = 3$?
   1. 4
   2. 12
   3. 16
   4. 20
7. If $z = 0.5$, evaluate $6z + 1$.
   1. 1
   2. 2
   3. 3
   4. 4