Pre-Algebra
Expressions and equations
Writing and evaluating algebraic expressions
20 practice questions
0 video lessons
Theory + worked examples
Writing and Evaluating Algebraic Expressions
Texas Pre-Algebra (TEKS) • Standard 6.7(A) • Expressions & Equations
Writing and Evaluating Algebraic Expressions is the opening topic of Expressions & Equations in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.7(A), which requires students to write and evaluate algebraic expressions.
An algebraic expression uses variables to represent numbers; you write one from words and evaluate it by substituting values.
Theory
An algebraic expression combines numbers, variables, and operations, such as \(3x+5\).
- A variable is a letter standing for a number.
- A coefficient multiplies a variable.
- A constant is a fixed number.
Evaluate by substituting values and simplifying.
The parts of an expression.
Key vocabulary.
Evaluating:
\[\text{substitute each variable, then simplify}\]
Use the order of operations when simplifying.
How to evaluate an expression
- Replace each variable with its value.
- Use parentheses around substitutions.
- Apply the order of operations.
- Simplify to a single number.
Example 1 — Write
Write “\(5\) more than \(3\) times \(n\).”
Solution
Translate the words.
| \(3n+5\) |
Example 2 — Evaluate
Evaluate \(3x+5\) at \(x=4\).
Solution
Substitute and simplify.
| \(3(4)+5\) | \(=\) | \(17\) |
Example 3 — Two variables
Evaluate \(2a-b\) at \(a=5,\ b=3\).
Solution
Substitute.
| \(2(5)-3\) | \(=\) | \(7\) |
Example 4 — Identify
Name the coefficient in \(7y\).
Solution
The number multiplying the variable.
| \(\text{coefficient}\) | \(=\) | \(7\) |
Common pitfalls
\(3x\) means \(3\cdot x\), not \(3\) next to \(x\).
Substitute with parentheses to keep signs right.
Follow the order of operations.
Frequently asked questions
What is an algebraic expression?
A combination of numbers, variables, and operations.
What does evaluate mean?
Substitute values and simplify.
Evaluate \(3x+5\) at \(x=4\).
\(17\).
What is a coefficient?
The number multiplying a variable.
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