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Jill solved the equation 8−p+7=7p−5−3p8 - p + 7 = 7p - 5 - 3p. Here are her last two steps:\newline20=5p20 = 5p\newline4=p4 = p\newlineWhich statement is true about the equation?\newlineChoices:\newline(A)The solution is p=4p = 4.\newline(B)There is no solution.\newline(C)There are infinitely many solutions.\newline(D)The solution is (20,4)(20, 4).

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Full solution

Q. Jill solved the equation 8−p+7=7p−5−3p8 - p + 7 = 7p - 5 - 3p. Here are her last two steps:\newline20=5p20 = 5p\newline4=p4 = p\newlineWhich statement is true about the equation?\newlineChoices:\newline(A)The solution is p=4p = 4.\newline(B)There is no solution.\newline(C)There are infinitely many solutions.\newline(D)The solution is (20,4)(20, 4).
  1. Simplify left side: First, simplify the left side of the equation by combining like terms: 8−p+78 - p + 7.
  2. Simplify right side: Next, simplify the right side of the equation: 7p−5−3p7p - 5 - 3p.
  3. Set equal: Now, set the simplified left side equal to the simplified right side: 15−p=4p−515 - p = 4p - 5.
  4. Isolate variable: Add pp to both sides and add 55 to both sides to isolate the variable pp: 15+5=4p+p15 + 5 = 4p + p.
  5. Solve for p: Divide both sides by 55 to solve for p: 205=p\frac{20}{5} = p.

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