Variables and Expressions: Practice

An equation has an equals sign joining two parts; an expression has none.

$4x - 1$

It names a value but makes no claim, so it is an expression. The other three all contain an equals sign.

"More than" means addition, and you add $7$ to the number $x$.

$x + 7$

The value $7$ is added on to whatever $x$ is.

Substitute $4$ for $x$, then add.

$(4) + 6 = 10$

So the expression is worth $10$.

The expression $5x$ means $5 \times x$. Substitute $3$ for $x$.

$5(3) = 15$

So the value is $15$, not the digits $5$ and $3$ written together.

"Less than $x$" means start at $x$ and take an amount away, so $x$ comes first.

$x - 3$

The order $3 - x$ is the common trap; the phrase says three less than $x$.

A constant is a term that is just a number, with no variable attached.

$4x + 9$

The term $9$ has no variable, so it is the constant. The $4$ is the coefficient of $4x$.

Substitute $7$ for $n$, then subtract.

$(7) - 2 = 5$

So the expression is worth $5$.

"Product" means multiplication, written without the times sign.

$6y = 6 \times y$

So the product of $6$ and $y$ is $6y$.

"Twice" means two times the number.

$2n = 2 \times n$

So twice the number $n$ is $2n$.

Substitute $5$ for $x$ and $8$ for $y$, then add.

$(5) + (8) = 13$

So the expression is worth $13$.

A variable is a placeholder for a number we do not yet know, or one that is free to change.

$x = \text{some number}$

The same letter can take different values on different occasions, which is why it is called a variable.

Substitute $2$ for $n$, then multiply before adding.

$3(2) + 1 = 6 + 1 = 7$

So the expression is worth $7$.