Forming and simplifying algebraic expressions

An expression is a mathematical phrase with no equals sign. An equation always contains an equals sign ($=$).

Go through each option: $5x+3=18$ has $=$, $y=2x-1$ has $=$, and $4a-9=0$ has $=$. Only $3n+7$ has no equals sign.

$3n+7$ is an algebraic expression — it contains a variable ($n$), a coefficient ($3$), a constant ($7$), and an operation ($+$), but no equals sign.

We need the option that is an expression, meaning it has no equals sign.

This contains an equals sign, so it is an equation, not an expression. Eliminate this option.

Both of these also contain equals signs, making them equations. Both are eliminated.

$3n+7$ has no equals sign — it is simply a mathematical phrase with a variable and a constant. This is the correct answer.

The coefficient is the number that is multiplied by the variable in a term. It sits directly in front of the letter.

In $8m+5$, the term containing the variable $m$ is $8m$. The number multiplied by $m$ is $8$.

The coefficient of $m$ is $8$. Note that $5$ is a constant (not a coefficient), and $m$ is the variable itself, not the coefficient.

We need the coefficient of $m$ in $8m+5$ — the number multiplied by $m$.

$5$ is the constant term in the expression — it stands alone with no variable. It is not a coefficient.

$m$ is the variable itself, not its coefficient. $13$ would come from adding $8+5$, but coefficients are not found by adding terms together.

$8$ is the number directly in front of $m$, making it the coefficient. The answer is $8$.