Evaluating Expressions

Q: What does $4x$ mean once $x = 5$?

Multiplication: $4x$ means $4$ times $x$, so it becomes $4(5) = 20$. It never means writing the digits side by side to get $45$.

An expression like $4x - 3$ doesn't have one fixed value — its value depends on what $x$ is. Evaluating an expression means substituting a specific value in for the variable and computing the result. It's the moment algebra turns back into arithmetic.

You'll evaluate expressions constantly: plugging numbers into formulas, checking whether a solution works, filling in a table before you graph. The skill is two moves — substitute, then compute — plus one habit that prevents nearly every sign error: wrap the substituted value in parentheses.

Substitute, then compute

Rewrite the expression with the value in place of the variable, inside parentheses. To evaluate $3x + 2$ at $x = 4$ , write $3(4) + 2$ . The parentheses keep the meaning clear: a number next to a variable means multiplication, so $3(4)$ is $12$ — never the digits pushed together into $34$ .

Then follow the order of operations, exactly as in arithmetic: multiply and divide before you add and subtract. $3(4) + 2$ becomes $12 + 2$ , which is $14$ .

Negative values need the parentheses most

With a negative value, the parentheses stop the signs from tangling. Evaluate $2x - 7$ at $x = -3$ : write $2(-3) - 7$ . The product is $-6$ , and $-6 - 7 = -13$ . Substituting without parentheses invites misreads like $2 - 3 - 7$ , which is a different computation entirely.

Keep the rules for integer arithmetic close: a positive times a negative is negative, and subtracting a number moves you further down the number line.

More than one variable

When an expression has two variables, each letter gets its own value. Substitute both at once, then compute as usual. For $4a + 3b$ with $a = 5$ and $b = -2$ : $4(5) + 3(-2) = 20 - 6 = 14$ . Write the substitution line before touching the arithmetic — skipping it is where values end up swapped.

Worked examples

Example 1: a positive value

Evaluate $3x + 2$ for $x = 4$ .

Substitute

4

in for

x

, in parentheses

3(4) + 2

Multiply first

12 + 2

Add

14

Answer: $14$

Example 2: a negative value

Evaluate $2x - 7$ for $x = -3$ .

Substitute

-3

in for

x

, in parentheses

2(-3) - 7

Multiply first — positive times negative is negative

-6 - 7

Subtract

-13

Answer: $-13$

Example 3: two variables

Evaluate $4a + 3b$ for $a = 5$ and $b = -2$ .

Substitute both values at once

4(5) + 3(-2)

Multiply each term

20 - 6

Combine

14

Answer: $14$

Try one yourself

Common questions

Why do I need parentheses when I substitute?

Two reasons. They preserve the multiplication — $3(4)$ can't be misread as $34$ — and they keep negative signs attached to their values, so $2(-3)$ stays a product of $2$ and $-3$ . It's one extra pen stroke that removes the two most common errors.

What does

4x

mean once

x = 5

Multiplication: $4x$ means $4$ times $x$ , so it becomes $4(5) = 20$ . It never means writing the digits side by side to get $45$ .

Which operation do I do first after substituting?

Follow the order of operations: parentheses, then multiplication and division from left to right, then addition and subtraction from left to right. In $4(5) + 3(-2)$ , both products are computed before anything is added.

What if the expression has two variables?

Each variable gets its own value — substitute them all in one step, then compute. In $4a + 3b$ with $a = 5$ and $b = -2$ , the $5$ replaces every $a$ and the $-2$ replaces every $b$ .

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Evaluating Expressions

Substitute, then compute

Negative values need the parentheses most

More than one variable

Worked examples

Example 1: a positive value

Example 2: a negative value

Example 3: two variables

Try one yourself

Common questions

Keep learning

Variables & Algebraic Expressions

Writing Expressions from Words

Order of Operations

Subtracting Integers