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Which pair of expressions has the same value?
A. (–2)(–7) and 4 + (–18)
B. (2)(7) and 4 + 18
C. (–2)(7) and 18 + (–4)
D. (2)(–7) and 4 – 18

Respuesta :

Option A)

Assuming that (-2)(-7) and 4 + (-18) are equal.

  • ⇒ (-2)(-7) = 4 + (-18)

Using the property [-x × -y = x × y = xy]:

  • ⇒ (-2)(-7) = 4 + (-18)
  • ⇒ (2)(7) = 4 + (-18)

Using the property [x + (-a) = x - a]:

  • ⇒ (2)(7) = 4 + (-18)
  • ⇒ (2)(7) = 4 - 18
  • ⇒ 14 = -14    (False)

Option B)

Assuming that (2)(7) and 4 + 18 are equal.

  • ⇒ (2)(7) = 4 + 18
  • ⇒ 14 = 22   (False)

Option C)

Assuming that (–2)(7) and 18 + (–4) are equal.

  • ⇒ (-2)(7) = 18 + (-4)

Using the property [-x × y = -xy]:

  • ⇒ (-2)(7) = 18 + (-4)
  • ⇒ (-)(2)(7) = 18 + (-4)
  • ⇒ -14 = 18 + (-4)

Using the property [x + (-a) = x - a]:

  • ⇒ -14 = 18 + (-4)
  • ⇒ -14 = 18 - 4
  • ⇒ -14 = 14   (False)

Option D)

Assuming that (2)(-7) and 4 - 18 are equal.

  • ⇒ (2)(-7) = 4 - 18

Using the property [-x × y = -xy]:

  • ⇒ (-)(2)(7) = 4 - 18
  • ⇒ -14 = 4 - 18
  • ⇒ -14 = -14   (True)

Therefore, Option D is correct.

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