Algebraic Expressions • Topic 2 of 3

Evaluating Expressions Given Variable Value

What Does "Evaluate" Mean?

To evaluate an expression means to substitute (replace) the variable with a number and then calculate the result.

Steps to Evaluate:

  1. Write the expression
  2. Replace each variable with its given value (use parentheses!)
  3. Follow order of operations (PEMDAS)
  4. Simplify to get a single number

Example: Evaluate 3x + 4 when x = 6

  • Write: 3x + 4
  • Substitute: 3(6) + 4
  • Calculate: 18 + 4 = 22
EVALUATING EXPRESSIONS - STEP BY STEP:

    Expression: 2n + 5, where n = 7
    
    Step 1: Write expression    2n + 5
    Step 2: Substitute n=7      2(7) + 5
    Step 3: Multiply first      14 + 5
    Step 4: Add                  19
    
    Answer: 19


EVALUATING WITH MULTIPLE VARIABLES:

    Expression: 3a + 2b, where a = 4, b = 5
    
    Step 1: 3a + 2b
    Step 2: 3(4) + 2(5)
    Step 3: 12 + 10
    Step 4: 22
    
    Answer: 22


EVALUATING WITH PARENTHESES:

    Expression: 2(x + 3), where x = 4
    
    Step 1: 2(x + 3)
    Step 2: 2(4 + 3)
    Step 3: 2(7) = 14
    
    Answer: 14


EVALUATING WITH EXPONENTS:

    Expression: x² + 3x - 2, where x = 5
    
    Step 1: x² + 3x - 2
    Step 2: 5² + 3(5) - 2
    Step 3: 25 + 15 - 2
    Step 4: 40 - 2 = 38
    
    Answer: 38
Solved Examples
1
Worked Example

Evaluate 4x - 7 when x = 9

Solution
  • Substitute: 4(9) - 7
  • Multiply: 36 - 7
  • Answer: 29
2
Worked Example

Evaluate 2a + 3b - c when a = 5, b = 4, c = 2

Solution
  • Substitute: 2(5) + 3(4) - 2
  • Multiply: 10 + 12 - 2
  • Add/Subtract: 22 - 2 = 20
  • Answer: 20
3
Worked Example

Evaluate 5(n - 3) + 2 when n = 10

Solution
  • Substitute: 5(10 - 3) + 2
  • Parentheses first: 5(7) + 2
  • Multiply: 35 + 2
  • Answer: 37
4
Worked Example

Evaluate (x² + 5) ÷ 3 when x = 7

Solution
  • Substitute: (7² + 5) ÷ 3
  • Exponent: (49 + 5) ÷ 3
  • Parentheses: 54 ÷ 3
  • Answer: 18

Key Points

  • Substitute variables with given numbers
  • Use parentheses when substituting (prevents errors)
  • Follow PEMDAS order of operations
  • Always show your steps
  • Check your arithmetic
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To evaluate an expression, you ___ the value of the variable.
Explanation: Substitute it.
Q2.$2x+1$ at $x=3$ is:
Explanation: $6+1=7$.
Q3.$x^2$ at $x=4$ is:
Explanation: $4^2$.
Q4.$3x$ at $x=5$ is:
Explanation: $15$.
Practice more MCQs → 📝 Assignment · 35 marks