Respuesta :

Part I: Converting the terms into fraction form

Given equation:

  • 3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.7

First, let's convert the terms (that are in decimals) into fractions.

  • 3.4k = 34k/10
  • 0.63 = 63/100
  • 0.81k = 81k/100
  • 0.9 = 9/10
  • 5.7 = 57/10

Replace the fraction forms in the equation:

  • 3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.7
  • 34k/10 + (63/100 - 81k/100) ÷ 9/10 = 57/10

Part II: Simplifying the division being performed

Since the expression in the parenthesis can't be simplified, we can open the parenthesis. Before we do that, we need to divide the expression by 9/10 (as division is third in BODMAS). This can be done by converting the divisor into it's reciprocal and changing the sign to a multiplication sign.

  • 34k/10 + (63/100 - 81k/100) × 10/9 = 57/10

Since there is no other division being performed, we can simplify the distributive property (as multiplication is fourth in BODMAS).

  • 34k/10 + [63/100 × 10/9] - [81k/100 × 10/9] = 57/10
  • 34k/10 + [7/10] - [9k/10] = 57/10
  • 34k/10 + 7/10 - 9k/10 = 57/10

Part III: Isolating "k" to determine it's value

Combine like terms as needed:

  • 34k/10 + 7/10 - 9k/10 = 57/10
  • k(34/10 - 9/10) + 7/10 = 57/10
  • 25k/10 + 7/10 = 57/10

Subtract 7/10 both sides of the equation to isolate "x" and it's coefficient.

  • 25k/10 + 7/10 - 7/10 = 57/10 - 7/10
  • 25k/10 = 50/10

Cancel the denominators (as a/b = c/b ⇔ a = c)

  • 25k/10 = 50/10
  • 25k = 50

Divide both sides by 25 to isolate "k"

  • 25k/25 = 50/25
  • k = 2

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