Evaluate the Expression for the Given Value of the Variable
What Does "Evaluate the Expression" Actually Mean?
It means plug in the given number for the variable and simplify. That's it. No tricks, no hidden steps.
When a problem says "evaluate 3x + 5 when x = 4," it's asking you to replace every x with 4, then calculate the result.
The answer is 3(4) + 5 = 12 + 5 = 17.
The Basic Process
Here's how to evaluate any algebraic expression:
- Write down the expression exactly as given
- Circle or highlight the variable you need to replace
- Substitute the given value in place of that variable
- Use parentheses around substituted numbers to avoid sign errors
- Simplify using order of operations (PEMDAS/BODMAS)
Why Parentheses Matter
When substituting negative numbers or fractions, parentheses prevent disasters.
Wrong approach: 2x² evaluated at x = -3 becomes 2-3² (completely wrong)
Right approach: 2(-3)² = 2(9) = 18
Examples: Easy to Hard
Single Variable, One Operation
Evaluate: 4y - 7 when y = 5
4(5) - 7 = 20 - 7 = 13
Negative Value Substitution
Evaluate: 2a + 3a - 10 when a = -2
2(-2) + 3(-2) - 10 = -4 - 6 - 10 = -20
Expression with Exponents
Evaluate: x² + 5x - 3 when x = 3
(3)² + 5(3) - 3 = 9 + 15 - 3 = 21
Fractional Values
Evaluate: 8m + 2 when m = 3/4
8(3/4) + 2 = 6 + 2 = 8
How To: Step-by-Step Evaluation
Let's walk through a complete example together.
Problem: Evaluate 2(x + 4) - 3x when x = 6
Step 1: Substitute the value
2(6 + 4) - 3(6)
Step 2: Work inside parentheses first
2(10) - 3(6)
Step 3: Multiply
20 - 18
Step 4: Subtract
Answer: 2
Common Mistakes That Blow the Answer
- Dropping the negative sign: When x = -4, don't write x² as -4². That's -16. Write (-4)² for 16.
- Ignoring the exponent: 3x² means 3 times x squared, not (3x)²
- Skipping the order of operations: Evaluate exponents before multiplication
- Forgetting distribution: 2(3 + x) = 6 + 2x, not 2x + 3
Evaluating Multiple Variables
Some problems give you more than one variable.
Problem: Evaluate 3x + 2y when x = 4 and y = -1
3(4) + 2(-1) = 12 - 2 = 10
Just substitute each variable with its corresponding value. Keep them separate.
Expression Types and Their Evaluation
| Expression Type | Example | When x = 2 | Answer |
|---|---|---|---|
| Linear | 5x + 3 | 5(2) + 3 | 13 |
| Quadratic | x² - 4 | (2)² - 4 | 0 |
| Polynomial | 2x³ + x | 2(8) + 2 | 18 |
| Fractional | (x + 3)/5 | (2 + 3)/5 | 1 |
Practice Problems
Evaluate each expression for the given value. Answers at the bottom.
- 7x + 2 when x = 3
- 12 - 3y when y = -4
- x² + 2x + 1 when x = 5
- 4(x - 3) when x = 7
- 5a - 2b when a = 3 and b = 4
Answers: 23 | 24 | 36 | 16 | 7
The Bottom Line
Evaluating expressions is substitution followed by simplification. Write the problem, plug in the number, calculate carefully.
Most errors come from rushing through the arithmetic or losing negative signs. Slow down on the multiplication and you'll get it right.