Evaluating and Simplifying Expressions: Practice

The two terms are alike, both being some number of $x$'s, so add the coefficients and keep the variable.

$3x + 4x = 7x$

The variable stays $x$; you never add the exponents or change the letter.

Substitute $4$ for $x$, writing it in parentheses, then multiply before you add.

$2(4) + 5 = 8 + 5 = 13$

The multiplication comes before the addition by the order of operations.

A plain $a$ means $1a$, so its coefficient is $1$. Add the coefficients.

$5a + 1a = 6a$

The invisible coefficient on $a$ is $1$, not $0$.

Add the coefficients of the like terms and keep the variable.

$8x + 2x = 10x$

The result is $10x$, not $10x^2$; the variable part does not change.

Like terms must share the same variable.

$4x \text{ uses } x, \text{ but } 4y \text{ uses } y$

The terms $7y$, $2y$, and $y$ all use $y$, so they are alike; only $4x$ is not.

Substitute $6$ for $x$ in parentheses, then multiply before subtracting.

$3(6) - 2 = 18 - 2 = 16$

The multiplication $3 \times 6$ runs before the subtraction.

Add the coefficients of the like terms.

$2x + 6x = 8x$

Keep the variable $x$ exactly as it is; do not multiply the coefficients.

Like terms share the same variable to the same power.

$2x \text{ and } 5x \text{ are both first-power } x \text{ terms}$

The other pairs differ in their variable, their power, or have no variable at all.

Substitute both values and add.

$(7) + (8) = 15$

The expression is a sum, so the two values are added, not multiplied or joined.

Add the coefficients of the two like terms.

$3b + 3b = 6b$

Adding $3b$ to itself doubles the coefficient to $6$; the variable stays $b$.

Distribute the $2$ across both terms inside.

$2(3x + 1) = 2 \cdot 3x + 2 \cdot 1 = 6x + 2$

The $2$ multiplies the $1$ to give $2$, and multiplies the coefficient $3$ to give $6$.

Substitute both values in parentheses, do each multiplication, then add.

$2(5) + 3(1) = 10 + 3 = 13$

Each coefficient multiplies its own variable before the two products are added.