Variables and Expressions: Additional Practice (Set 1)

The product of $4$ and the number is $4x$, and three more than that adds $3$.

$4x + 3$

The $3$ is added after the multiplication.

Substitute, add inside the parentheses first, then multiply by $2$.

$2(5 + 3) = 2(8) = 16$

The whole sum is doubled.

The minus sign belongs to the term it sits in front of, so the $x$ term is $-3x$.

$-3x = -3 \times x$

The coefficient is $-3$.

Substitute $4$, square first, then subtract from $10$.

$10 - (4)^2 = 10 - 16 = -6$

The square $16$ is larger than $10$, so the result is negative.

Substitute $6$ into each fraction, then add the two results.

$\frac{6}{3} + \frac{6}{2} = 2 + 3 = 5$

So the value is $5$.

The exponent $3$ means three factors of the value of $x$.

$(2)^3 = 2 \times 2 \times 2 = 8$

So the value is $8$, not $2 \times 3 = 6$.

The equals sign joining the two sides makes it an equation, not an expression.

$9 = 4x + 1$

An equation is solved, while an expression alone is evaluated.

Substitute $2$, square and multiply each term, then combine left to right.

$2(2)^2 + 3(2) - 1 = 2(4) + 6 - 1 = 8 + 6 - 1 = 13$

So the value is $13$.

Substitute $4$ for $x$, divide first, then subtract.

$\frac{12}{4} - 1 = 3 - 1 = 2$

So the value is $2$.

Twice the number is $2x$, and half of the number is $\dfrac{x}{2}$, which is subtracted.

$2x - \frac{x}{2}$

Both pieces involve the same variable $x$.

Substitute, square each variable separately, then subtract.

$(6)^2 - (4)^2 = 36 - 16 = 20$

Each square is found before subtracting.

Substitute $-3$, keeping it in parentheses, then multiply and add.

$-2(-3) + 5 = 6 + 5 = 11$

A negative times a negative gives the positive $6$, then $5$ is added.