Math

QuestionFind equivalent expressions for 2(j+9)-2(j+9). Options: (j+9)2(j+9) \cdot-2, 2(9+j)-2(9+j), 2j18-2 j-18, 7j7 j.

Studdy Solution

STEP 1

Assumptions1. The expression we are comparing to is (j+9)-(j+9). We are looking for expressions that are equivalent to this3. The properties of real numbers apply, including the commutative property of addition (changing the order does not change the sum), and the distributive property of multiplication over addition (multiplying a sum by a number is the same as multiplying each addend separately by the number and then adding the products)

STEP 2

First, let's distribute the 2-2 in the expression 2(j+9)-2(j+9) to each term inside the parentheses.
2(j+9)=2j+29-2(j+9) = -2 \cdot j + -2 \cdot9

STEP 3

Perform the multiplication to simplify the expression.
2(j+9)=2j18-2(j+9) = -2j -18

STEP 4

Now, let's compare this to each of the given expressions.The first expression is (j+9)2(j+9) \cdot -2. This is the same as 2(j+9)-2(j+9) because multiplication is commutative, meaning the order of the factors does not change the product. So, (j+9)2(j+9) \cdot -2 is equivalent to 2(j+9)-2(j+9).

STEP 5

The second expression is 2(9+j)-2(9+j). This is the same as 2(j+9)-2(j+9) because addition is commutative, meaning the order of the terms does not change the sum. So, 2(9+j)-2(9+j) is equivalent to 2(j+9)-2(j+9).

STEP 6

The third expression is 2j18-2j -18. This is the same as 2(j+9)-2(j+9) because it is the result of distributing 2-2 to each term inside the parentheses in 2(j+9)-2(j+9), as we calculated in3. So, 2j18-2j -18 is equivalent to 2(j+9)-2(j+9).

STEP 7

The fourth expression is 7j7j. This is not the same as 2(j+9)-2(j+9) because the coefficient of jj is different and there is no constant term in 7j7j. So, 7j7j is not equivalent to 2(j+9)-2(j+9).
Therefore, the expressions equivalent to 2(j+9)-2(j+9) are (j+9)2(j+9) \cdot -2, 2(9+j)-2(9+j), and 2j18-2j -18.

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