Writing and Evaluating Expressions

Variables

A variable is a letter that represents an unknown number: $x$, $y$, $n$, etc.

Algebraic Expressions

An expression combines numbers, variables, and operations:

• $3x + 5$ means "3 times $x$ plus 5"
• $2(n - 4)$ means "2 times the quantity $n$ minus 4"

Translating Words to Expressions

| Words | Expression | |-------|-----------| | A number plus 7 | $n + 7$ | | 5 less than a number | $n - 5$ | | 3 times a number | $3n$ | | A number divided by 4 | $\frac{n}{4}$ | | Twice a number increased by 1 | $2n + 1$ |

Evaluating Expressions

Substitute the given value and compute:

Evaluate $3x + 7$ when $x = 4$: $3(4) + 7 = 12 + 7 = 19$

Evaluate $x^2 - 2x$ when $x = 5$: $5^2 - 2(5) = 25 - 10 = 15$

Parts of an Expression

• Term: Parts separated by $+$ or $-$ signs
• Coefficient: The number multiplied by a variable ($3x$ → coefficient is 3)
• Constant: A term without a variable ($+5$)

In $4x + 3y - 7$:

• Terms: $4x$, $3y$, $-7$
• Coefficients: 4, 3
• Constant: $-7$

Properties

• Commutative: $a + b = b + a$ and $ab = ba$
• Associative: $(a + b) + c = a + (b + c)$
• Distributive: $a(b + c) = ab + ac$

Remember: $5n$ means $5 \times n$. In algebra, we usually skip the multiplication sign.