QuestionFind expressions equivalent to $2(-2 j+7)$ . Options include: $-4 j+7$ , $2(-4 j+2 j+7)$ , $-4 j+14$ , $14 j-4$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(- j+7)$ . We are asked to find the expressions equivalent to this given expression

STEP 2

First, we need to simplify the given expression. We can do this by distributing the $2$ to each term inside the parentheses.
$2(-2 j+7) =2 \times -2j +2 \times7$

STEP 3

Now, calculate each term separately.
$2 \times -2j = -j$ $2 \times7 =14$

STEP 4

Combine these terms to get the simplified form of the given expression.
$2(-2 j+7) = -4j +14$

STEP 5

Now, we compare this simplified expression with the given options. The expressions equivalent to $-4j +14$ are the correct answers.
The first option is $-4 j+7$ , which is not equivalent to $-4j +14$ .
The second option is $2(-4 j+2 j+7)$ , which simplifies to $-4j +14$ , so it is equivalent.
The third option is $-4 j+14$ , which is exactly the same as our simplified expression, so it is equivalent.
The fourth option is $14 j-4$ , which is not equivalent to $-4j +14$ .
So, the expressions equivalent to $2(-2 j+7)$ are $2(-4 j+2 j+7)$ and $-4 j+14$ .

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