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Which expressions are equivalent to 4d+6+2d ?
Choose all answers that apply:
(A) 2(3d+3)
(B) 6(d+6)
(C) (3d+3)+(3d+3)

Which expressions are equivalent to $4 d+6+2 d$ ? $\newline$ Choose all answers that apply: $\newline$ (A) $2(3 d+3)$ $\newline$ (B) $6(d+6)$ $\newline$ (C) $(3 d+3)+(3 d+3)$

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Find the magnitude of a vector

Full solution

Q. Which expressions are equivalent to

4 d+6+2 d

?

\newline

Choose all answers that apply:

\newline

(A)

2(3 d+3)

\newline

(B)

6(d+6)

\newline

(C)

(3 d+3)+(3 d+3)

Simplify Expression: First, we need to simplify the given expression by combining like terms. $\newline$ $4d + 6 + 2d$ can be simplified by adding the 'd' terms together. $\newline$ $4d + 2d = 6d$ $\newline$ So the simplified expression is $6d + 6$ .
Check Option A: Now let's check each answer choice to see if it is equivalent to the simplified expression $6d + 6$ . $\newline$ Option A: $2(3d+3)$ $\newline$ We distribute the $2$ into the parentheses. $\newline$ $2 \times 3d = 6d$ $\newline$ $2 \times 3 = 6$ $\newline$ So, $2(3d+3)$ simplifies to $6d + 6$ .
Check Option B: Option B: $6(d+6)$ $\newline$ We distribute the $6$ into the parentheses. $\newline$ $6 \times d = 6d$ $\newline$ $6 \times 6 = 36$ $\newline$ So, $6(d+6)$ simplifies to $6d + 36$ , which is not equivalent to $6d + 6$ .
Check Option C: Option C: $3d+3)+(3d+3)(\newline$ We combine like terms. $\newline$ \$3d + 3d = 6d\)\(\newline\)\(3 + 3 = 6\)\(\newline\)So, \(3d+3)+(3d+3)\ simplifies to \$6d + 6\).

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