Question

use the distributive property to match equivalent expressions.
-7(-4 + x)
-7(4 - x)
7(-4 - x)
7(4 + x)
28 + 7x
-28 + 7x
-28 - 7x
28 - 7x

Explanation:

Step1: Distribute -7 to (-4+x)

$$\begin{align*} -7(-4 + x) &= (-7)(-4) + (-7)(x) \\ &= 28 - 7x \end{align*}$$

Step2: Distribute -7 to (4-x)

$$\begin{align*} -7(4 - x) &= (-7)(4) + (-7)(-x) \\ &= -28 + 7x \end{align*}$$

Step3: Distribute 7 to (-4-x)

$$\begin{align*} 7(-4 - x) &= (7)(-4) + (7)(-x) \\ &= -28 - 7x \end{align*}$$

Step4: Distribute 7 to (4+x)

$$\begin{align*} 7(4 + x) &= (7)(4) + (7)(x) \\ &= 28 + 7x \end{align*}$$

Answer:

$-7(-4 + x) \longleftrightarrow 28 - 7x$
$-7(4 - x) \longleftrightarrow -28 + 7x$
$7(-4 - x) \longleftrightarrow -28 - 7x$
$7(4 + x) \longleftrightarrow 28 + 7x$