Evaluating and Simplifying Expressions: Practice

Distribute the $2$ first, then combine the like terms.

$2(x + 3) + x = 2x + 6 + x = 3x + 6$

The $2x$ from distributing and the outside $x$ are like terms, so they collect into $3x$.

Combine the $x$-terms; the $y$-term has nothing like to combine with.

$4x - x + 2y = 3x + 2y$

The $x$-terms and the $y$-term stay separate, since they are unlike.

Substitute $3$ for $x$. By the order of operations, square before multiplying by $2$.

$2(3)^2 = 2 \cdot 9 = 18$

The exponent applies only to the $3$, so square first and the coefficient $2$ multiplies the result.

Combine the $x$-terms and keep the constant.

$7x - 2x + 5 = 5x + 5$

Only the $x$-terms combine; the $5$ is unlike and remains.

Distribute both factors, then combine like terms.

$(4x + 8) + (3x + 3) = 7x + 11$

The $x$-terms give $4x + 3x = 7x$ and the constants give $8 + 3 = 11$.

Combine the $x$-terms, keeping each sign, and leave the constant.

$-3x + 2x = -x, \qquad \text{so} \qquad 10 - 3x + 2x = 10 - x$

Adding $-3x$ and $2x$ gives $-1x$, written $-x$.

Group the $x$-terms and the constants separately, keeping each sign.

$(8x - 5x) + (3 - 1) = 3x + 2$

The $x$-terms give $3x$ and the constants give $2$.

Combine the $y$-terms and the constants separately.

$(3y + 2y) + (4 + 1) = 5y + 5$

The $y$-terms give $5y$ and the constants give $5$.

Distribute the $2$, then combine the $x$-terms.

$x + 2x + 10 = 3x + 10$

The outside $x$ and the $2x$ from distributing combine into $3x$.

Substitute $-2$ for $x$ in parentheses, multiply, then subtract.

$4(-2) - 1 = -8 - 1 = -9$

A positive coefficient on a negative input gives $-8$, and subtracting $1$ moves further down to $-9$.

Distribute both factors, then combine like terms.

$(6x + 4) + (2x - 2) = 8x + 2$

The $x$-terms give $8x$ and the constants give $4 - 2 = 2$.

Substitute both values, then finish inside the parentheses before multiplying.

$2\big((3) + (4)\big) = 2(7) = 14$

The sum $3 + 4 = 7$ is completed first because it is grouped, then doubled.