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Select the TWO expressions that are equivalent to this algebraic expression:

−5(3x−9)

(2 points)
Responses

−15x−9

−15x+45

−15x−45

15x−9

−5×3x−5×9

5×3x+9

−5×3x+−5×(−9)

1 answer

To simplify the expression \(-5(3x - 9)\):

  1. Distribute \(-5\) to both terms inside the parentheses:

\[ -5 \cdot 3x + -5 \cdot (-9) = -15x + 45 \]

So, \(-5(3x - 9)\) simplifies to \(-15x + 45\).

Now we will look for equivalent expressions:

  1. \(-5 \times 3x - 5 \times 9\):

    • This expression simplifies to: \[ -15x - 45 \] (This is not equivalent to \(-15x + 45\)).

  2. \(-15x + 45\):

    • This is exactly what we found during simplification.

  3. \(-15x - 9\):

    • This is not equivalent to \(-15x + 45\) (since the constant term is different).

  4. \(15x - 9\):

    • This is also not equivalent to \(-15x + 45\).

  5. \(5 \times 3x + 9\):

    • This simplifies to: \[ 15x + 9 \] (This is not equivalent to \(-15x + 45\)).

  6. \(-5 \times 3x + -5 \times (-9)\):

    • This simplifies to: \[ -15x + 45 \] (This matches our simplified result).

Thus, the two expressions that are equivalent to \(-5(3x - 9)\) are:

  • \(-15x + 45\)
  • \(-5 \times 3x + -5 \times (-9)\)