Algebra
Expressions
Evaluating expressions
20 practice questions
2 video lessons
Theory + worked examples
Theory
To evaluate an expression, replace each variable with its value and simplify using the order of operations:
- Parentheses, Exponents,
- Multiply / Divide (left to right),
- Add / Subtract (left to right).
Use parentheses around substituted values, especially negatives.
Substitute, then simplify by PEMDAS.
The order of operations.
The order of operations:
\[\text{P}\to\text{E}\to\text{MD}\to\text{AS}\]
Multiply/divide before add/subtract.
How to evaluate
- Substitute each value (use parentheses).
- Simplify inside parentheses.
- Apply exponents.
- Multiply/divide, then add/subtract.
Example 1 — One variable
Evaluate \(3x+4\) when \(x=5\).
Solution
Substitute and simplify.
| \(3(5)+4\) | \(=\) | \(15+4\) |
| \(=\) | \(19\) |
Example 2 — Two variables
Evaluate \(2a-b\) when \(a=6,\ b=4\).
Solution
Substitute both values.
| \(2(6)-4\) | \(=\) | \(12-4\) |
| \(=\) | \(8\) |
Example 3 — With an exponent
Evaluate \(x^2-2x\) when \(x=3\).
Solution
Exponents before subtraction.
| \(3^2-2(3)\) | \(=\) | \(9-6\) |
| \(=\) | \(3\) |
Example 4 — A negative value
Evaluate \(5-2x\) when \(x=-1\).
Solution
Substitute carefully with the sign.
| \(5-2(-1)\) | \(=\) | \(5+2\) |
| \(=\) | \(7\) |
Common pitfalls
Follow PEMDAS — don't just work left to right.
Use parentheses for negatives: \(2(-1)=-2\).
Exponent applies to the base only unless parenthesized.
Frequently asked questions
What does it mean to evaluate an expression?
Substitute values for the variables and simplify to a number.
What is the order of operations?
PEMDAS: parentheses, exponents, multiply/divide, add/subtract.
Why use parentheses when substituting?
To keep signs and multiplication correct, especially for negatives.
Evaluate \(2x\) at \(x=-3\).
\(2(-3)=-6\).
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