6A Write & Evaluate Expressions Study Guide

Key Vocabulary

Expression — a math phrase with numbers, variables, and operations (no = sign). (expresión)

Variable — a letter (like x or n) that stands for an unknown number. (variable)

Evaluate — to find the value of an expression by replacing the variable with a number. (evaluar)

Substitute — to replace a variable with a given number. (sustituir)

Coefficient — the number multiplied by a variable (in 5x, the coefficient is 5). (coeficiente)

Constant — a number that stands alone (no variable attached). (constante)

Writing an expression from words:

"Three more than a number" → n + 3
"Twice a number" → 2n
"A number divided by 4" → n ÷ 4 or n/4

Evaluating an expression:

Evaluate 3x + 7 when x = 4
Step 1: Replace x with 4 → 3(4) + 7
Step 2: Multiply → 12 + 7
Step 3: Add → 19

1 Read the words carefully. Find the key math words (sum, product, difference, quotient).
2 Choose a variable for the unknown number.
3 Write the expression using numbers, the variable, and the operation.

P → Parentheses first
E → Exponents
M/D → Multiply and Divide (left to right)
A/S → Add and Subtract (left to right)

An expression is NOT an equation. Expressions have no equals sign (=). Equations do.
"5 less than x" = x − 5, NOT 5 − x. The order matters with subtraction!
"Twice a number" = 2n. In algebra, we write the number before the variable (not n2).
Always follow order of operations when evaluating. Multiply before you add!

1. Evaluate 2x + 5 when x = 6.

2. Evaluate 4(n − 3) when n = 10.

3. Write an expression for: "8 more than twice a number." Use n for the variable. (Example format: 2n+8)

4. Evaluate 10 − x/2 when x = 4.