Question

equivalent linear expressions — instruction — level g
are the expressions $4f + (-21) + 10f$ and $-7(-2f + 3)$ equivalent?
show why or why not.

first combine the like terms in $4f + (-21) + 10f$.
$4f + (-21) + 10f = 14f + (-21)$

which factored expressions are equivalent to $14f + (-21)$?
choose all that apply.
$-7(-2f + 3)$ $7(2f - 3)$

complete the statement.

the expressions $4f + (-21) + 10f$ and $-7(-2f + 3)$ ? equivalent.
are
are not

Explanation:

Step1: Simplify first expression

$4f + (-21) + 10f = (4f+10f) -21 = 14f -21$

Step2: Expand second expression

$-7(-2f + 3) = (-7)(-2f) + (-7)(3) = 14f -21$

Step3: Compare the two results

Both expressions simplify to $14f -21$.

Step4: Verify factored forms

For $14f-21$:

• $-7(-2f+3)=14f-21$
• $7(2f-3)=14f-21$

Both factored expressions match.

Answer:

1. The factored expressions equivalent to $14f + (-21)$ are:

• $-7(-2f + 3)$
• $7(2f - 3)$

1. The expressions $4f + (-21) + 10f$ and $-7(-2f + 3)$ are equivalent.