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Which expression correctly demonstrates the Commutative Property of Multiplication?(1 point) Responses 15⋅(x)⋅4=4⋅15⋅(x) 15 times left parenthesis x right parenthesis times 4 equals 4 times 15 times left parenthesis x right parenthesis x+4+15=15+4+x x plus 4 plus 15 equals 15 plus 4 plus x 15(x+4)=15(x⋅4) 15 left parenthesis x plus 4 right parenthesis equals 15 left parenthesis x times 4 right parenthesis 15⋅x⋅4=4+15+x

5 answers

The Commutative Property of Multiplication states that changing the order of the factors does not change the product.

The expression that correctly demonstrates the Commutative Property of Multiplication from your provided options is:

15⋅(x)⋅4 = 4⋅15⋅(x)

This shows that you can rearrange the factors (15, x, and 4) without changing the product.

Which expression is equivalent to −3x−5 ?(1 point) Responses (−4x−6)+(2+5x) left parenthesis negative 4 x minus 6 right parenthesis plus left parenthesis 2 plus 5 x right parenthesis −1+(x−4x)+6 negative 1 plus left parenthesis x minus 4 x right parenthesis plus 6 −1+3x−(2x+6) negative 1 plus 3 x minus left parenthesis 2 x plus 6 right parenthesis (x−7)+(2−4x)

To find which expression is equivalent to \(-3x - 5\), we need to simplify each response option and see which one matches.

Let's analyze each option:

  1. \((-4x - 6) + (2 + 5x)\): \[ -4x - 6 + 2 + 5x = (-4x + 5x) + (-6 + 2) = 1x - 4 = x - 4 \quad (\text{not equivalent}) \]

  2. \(-1 + (x - 4x) + 6\): \[ -1 + (x - 4x) + 6 = -1 + (-3x) + 6 = -3x + 5 \quad (\text{not equivalent}) \]

  3. \(-1 + 3x - (2x + 6)\): \[ -1 + 3x - 2x - 6 = 3x - 2x - 1 - 6 = 1x - 7 = x - 7 \quad (\text{not equivalent}) \]

  4. \((x - 7) + (2 - 4x)\): \[ (x - 7) + (2 - 4x) = x - 7 + 2 - 4x = x - 4x - 7 + 2 = -3x - 5 \quad (\text{equivalent!}) \]

The only expression that is equivalent to \(-3x - 5\) is:

\((x - 7) + (2 - 4x)\).

Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2. Expression 1: 22r−13 Expression 2: 19r+(3r−2)−11

To demonstrate that Expression 1: \( 22r - 13 \) is equivalent to Expression 2: \( 19r + (3r - 2) - 11 \) using the Associative Property, we will simplify Expression 2 step by step.

Expression 2:

\[ 19r + (3r - 2) - 11 \]

  1. Start by simplifying the expression inside the parentheses: \[ = 19r + 3r - 2 - 11 \]

  2. Combine like terms (the \(r\) terms and the constant terms):

    • Combine the \(r\) terms: \[ 19r + 3r = 22r \]
    • Combine the constant terms: \[ -2 - 11 = -13 \]

  3. Putting it all together: \[ = 22r - 13 \]

Now, we have simplified Expression 2 to: \[ 22r - 13 \]

Conclusion:

Both expressions simplify to the same result:

  • Expression 1: \( 22r - 13 \)
  • Expression 2: \( 22r - 13 \)

Thus, using the Associative Property (which allows us to group terms differently when adding or subtracting), we have demonstrated that Expression 1 is equivalent to Expression 2: \[ 22r - 13 = 19r + (3r - 2) - 11 \]