QuestionWhich property is not used to simplify $2 \cdot(x+5)+7 x$ to $9 x+10$ ? Options: distributive, commutative (addition/multiplication).

Studdy Solution

STEP 1

Assumptions1. The given expression is $\cdot(x+5)+7 x = ( x+10)+7 x = (10+ x)+7 x =10+( x+7 x) =10+9 x =9 x+10$ . . We are asked to identify which property is not used to simplify the expression.
3. The properties under consideration are the distributive property, the commutative property of addition, and the commutative property of multiplication.

STEP 2

Let's start by identifying where each property is used in the expression.
The distributive property is used in the first step of the simplification $2 \cdot(x+5)+7 x = (2 x+10)+7 x$ This is because $2 \cdot(x+5)$ is distributed as $2x +10$ .

STEP 3

The commutative property of addition is used in the second and the last step of the simplification $(2 x+10)+7 x = (10+2 x)+7 x$ $10+9 x =9 x+10$ This is because the order of addition does not affect the result.

STEP 4

Now, let's look for the use of the commutative property of multiplication in the simplification. The commutative property of multiplication states that the order of multiplication does not affect the result, i.e., $a \cdot b = b \cdot a$ .
However, in the given expression, there are no instances where the order of multiplication is changed. Therefore, the commutative property of multiplication is not used to simplify the given expression.
The property not used to simplify the expression is the commutative property of multiplication.

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