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Find the solution set of 16x +24 = 7x + 60 Consider the replacement set {-2, 4, 9}, whose values or elements are arbitrarily given.​

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Problem:

Find the solution set of 16x +24 = 7x + 60 Consider the replacement set {-2, 4, 9}, whose values or elements are arbitrarily given.

Solution:

Replace the x with -2, then 4, and 9 to the equation of 16x +24 = 7x + 60.

Substitute the equation if x = -2.

  • 16x +24 = 7x + 60
  • 16(-2) +24 = 7(-2) + 60
  • -32 + 24 = -14 + 60
  • -8 ≠ 46
  • -8 = 46 is False

Substitute the equation if x = 4.

  • 16x +24 = 7x + 60
  • 16(4) +24 = 7(4) + 60
  • 64 + 24 = 28 + 60
  • 88 = 88
  • 88 = 88 is True

Substitute the equation if x = 9.

  • 16x +24 = 7x + 60
  • 16(9) +24 = 7(9) + 60
  • 144 + 24 = 63 + 60
  • 168 ≠ 123
  • 168 = 123 is False

Answer:

∴ Only the replacement of x with 4 in the equation makes the sentence true. Therefore, the solution of 16x +24 = 7x + 60 is {4}.

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