Variables and Expressions: Practice

Twice the number is $2x$, and eight more than that adds $8$.

$2x + 8$

The $8$ is added on after doubling, not doubled itself.

Substitute $4$ for $x$, then square before adding.

$(4)^2 + 1 = 16 + 1 = 17$

The exponent acts on the $4$ first, then the $1$ is added.

Substitute $4$ for $a$ and $1$ for $b$, then multiply each term before adding.

$2(4) + 3(1) = 8 + 3 = 11$

So the value is $11$.

Dividing by $3$ is the same as multiplying by $\dfrac{1}{3}$.

$\frac{x}{3} = \frac{1}{3}\,x$

So the coefficient is $\dfrac{1}{3}$.

Three times the number is $3n$, and five less than that subtracts $5$.

$3n - 5$

The $3n$ comes first because the phrase is five less than it, not the other way around.

A negative sign in front of a bare variable means a coefficient of $-1$, because $-x$ is $-1x$.

$-x = -1x$

So the coefficient is $-1$.

Substitute $5$ for $a$ and $9$ for $b$, squaring first.

$(5)^2 - (9) = 25 - 9 = 16$

The exponent applies only to $a$, then $b$ is subtracted.

Substitute $6$ for $x$ and $3$ for $y$, multiplying the first term before adding.

$2(6) + (3) = 12 + 3 = 15$

So the value is $15$.

Substitute $8$ for $x$, divide first, then add.

$\frac{8}{2} + 5 = 4 + 5 = 9$

So the value is $9$.

The sum is $x + 3$, and multiplying the whole sum by $5$ needs parentheses.

$5(x + 3)$

The parentheses keep the entire sum together before multiplying.

Substitute $3$ for $n$, multiply first, then subtract.

$10 - 2(3) = 10 - 6 = 4$

The multiplication $2 \times 3$ comes before the subtraction.

Substitute $2$ for $a$ and $5$ for $b$, multiplying each term before adding.

$3(2) + 2(5) = 6 + 10 = 16$

So the value is $16$.