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Select all of the equations below that are equivalent to:\newlineqr=13qr = 13\newlineUse properties of equality.\newline\newlineMulti-select Choices:\newline(A) qr4=10qr - 4 = 10\newline(B) qr4=9qr - 4 = 9\newline(C) qr2=13qr - 2 = 13\newline(D) qr3=9qr - 3 = 9

Full solution

Q. Select all of the equations below that are equivalent to:\newlineqr=13qr = 13\newlineUse properties of equality.\newline\newlineMulti-select Choices:\newline(A) qr4=10qr - 4 = 10\newline(B) qr4=9qr - 4 = 9\newline(C) qr2=13qr - 2 = 13\newline(D) qr3=9qr - 3 = 9
  1. Start with Original Equation: To determine if an equation is equivalent to qr=13qr = 13, we can manipulate the original equation and compare it to the choices given. We start with the original equation:\newlineqr=13qr = 13
  2. Compare with Choice (A): Now let's compare the original equation to choice (A): \newlineqr4=10qr - 4 = 10\newlineTo check if this is equivalent, we can add 44 to both sides of the equation qr=13qr = 13:\newlineqr+4=13+4qr + 4 = 13 + 4\newlineqr+4=17qr + 4 = 17\newlineThis is not equal to 1010, so choice (A) is not equivalent to qr=13qr = 13.
  3. Compare with Choice (B): Next, we compare the original equation to choice (B):
    qr4=9qr - 4 = 9
    Again, we add 44 to both sides of the equation qr=13qr = 13:
    qr+4=13+4qr + 4 = 13 + 4
    qr+4=17qr + 4 = 17
    This is not equal to 99, so choice (B) is not equivalent to qr=13qr = 13.
  4. Compare with Choice (C): Now we compare the original equation to choice (C):
    qr2=13qr - 2 = 13
    To check if this is equivalent, we can add 22 to both sides of the equation qr=13qr = 13:
    qr+2=13+2qr + 2 = 13 + 2
    qr+2=15qr + 2 = 15
    This is not equal to 1313, so choice (C) is not equivalent to qr=13qr = 13.
  5. Compare with Choice (D): Finally, we compare the original equation to choice (D):
    qr3=9qr - 3 = 9
    To check if this is equivalent, we can add 33 to both sides of the equation qr=13qr = 13:
    qr+3=13+3qr + 3 = 13 + 3
    qr+3=16qr + 3 = 16
    This is not equal to 99, so choice (D) is not equivalent to qr=13qr = 13.

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