Evaluating and Simplifying Expressions: Practice

Distribute each factor, watching that the $-3$ multiplies both terms of the second group.

$(6x - 2) + (-3x - 6) = 3x - 8$

The $x$-terms give $6x - 3x = 3x$ and the constants give $-2 - 6 = -8$.

Distribute the $-2$ across $(x - 5)$, flipping signs, then combine the $x$-terms.

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

The negative times $-5$ gives $+10$, and $-2x + 3x = x$.

Distribute the $-2$ across $(3 - x)$, then combine the constants.

$5 - 6 + 2x = 2x - 1$

The $-2$ times $-x$ gives $+2x$, and $5 - 6 = -1$.

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

$3x + 2x - 8 - 5 = 5x - 13$

The $x$-terms give $5x$ and the constants give $-8 - 5 = -13$.

Distribute both factors, watching that the $-2$ flips the signs of the second group.

$(4x + 4) + (-2x + 6) = 2x + 10$

The $-2$ times $-3$ gives $+6$, so the constants total $4 + 6 = 10$.

Substitute both values in parentheses and square each before subtracting.

$(5)^2 - (3)^2 = 25 - 9 = 16$

Each square is found first, then $25 - 9 = 16$. This is not $(5 - 3)^2 = 4$.

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

$10 - 2x - 6 - x = 4 - 3x$

The $x$-terms give $-2x - x = -3x$ and the constants give $10 - 6 = 4$.

Substitute both values, finish inside the parentheses first, then multiply.

$3\big((2) - (7)\big) = 3(-5) = -15$

The difference $2 - 7 = -5$ is found first, then $3 \times (-5) = -15$.

Dividing by $3$ divides every term of the numerator, the distributive rule for division.

$\frac{6x}{3} + \frac{9}{3} = 2x + 3$

Both terms are divided, so $6x \div 3 = 2x$ and $9 \div 3 = 3$.

Distribute the $-3$, then combine the $x$-terms and the constants.

$7 - 3x + 6 + x = 13 - 2x$

The $-3$ times $-2$ gives $+6$, the $x$-terms give $-2x$, and $7 + 6 = 13$.

Distribute both factors, then combine the $x$-terms and the $y$-terms separately.

$6x + 3y - 2x + 2y = 4x + 5y$

The $-2$ times $-y$ gives $+2y$, so the $y$-terms total $3y + 2y = 5y$.

Substitute $4$ for each $x$, finishing the numerator and denominator before dividing.

$\frac{(4) + 10}{(4) - 1} = \frac{14}{3}$

The fraction bar groups top and bottom, so each is computed first; $\tfrac{14}{3}$ does not reduce.