The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
From words to symbols
A variable is a letter that stands for an unknown number. "Five more than a number" becomes n + 5. "Three times a number, minus 7" becomes 3n − 7.
Evaluating an expression
To evaluate, substitute the given value for the variable and simplify using the order of operations.
An expression is a math phrase without an equals sign. It can be evaluated when you know the value of the variable.
Like terms have the same variable raised to the same power. You can only combine like terms: 3x and 5x combine, but 3x and 3y do not.
Evaluate 2x + 5 when x = 4.
- 1Substitute: 2(4) + 5.
- 2Multiply first: 8 + 5.
- 3Add: 13.
Why this matters
Turn word phrases into math, then plug in numbers to evaluate.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Doing different operations to each side of an equation. Whatever you add, subtract, multiply, or divide on one side, do to the other.
Combining unlike terms (like 3x and 4) as if they were the same kind of term.
Key ideas from this lesson
- From words to symbols
- Evaluating an expression
Video walkthroughs
Writing Expressions with Variables
Turn word phrases like "five more than x" into algebra.
Watch on YouTube
Evaluating Expressions with Exponents
Plug in values for variables and follow order of operations.
Watch on YouTube
Evaluating Expressions with Two Variables
Substitute two values and simplify a variable expression.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfWrite an expression for "a number plus 11."
Step-by-step solution
- 1Use a variable for the number, such as n.
- 2Plus 11 gives n + 11.
Exercise 2
Try it yourselfWrite an expression for "7 less than a number."
Step-by-step solution
- 1Let the number be x.
- 2"7 less than" means x − 7, not 7 − x.
Exercise 3
Try it yourselfEvaluate 4a − 6 when a = 5.
Step-by-step solution
- 1Substitute: 4(5) − 6.
- 2Multiply: 20 − 6 = 14.
Exercise 4
Try it yourselfWrite an expression for "twice a number, decreased by 3."
Step-by-step solution
- 1Twice a number is 2n.
- 2Decreased by 3 means subtract 3: 2n − 3.
Exercise 5
Try it yourselfEvaluate 3(x + 2) − x when x = 4.
Step-by-step solution
- 1Substitute: 3(4 + 2) − 4 = 3(6) − 4.
- 2Multiply: 18 − 4 = 14.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Writing Algebraic Expressions
Question 1 of 5
Write an expression for "twice a number plus 9."