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Matt solved the equation 3(z+1)2=4zz13(z + 1) - 2 = 4z - z - 1. Here are his last two steps:\newline3z+1=3z13z + 1 = 3z - 1\newline1=11 = -1\newlineWhich statement is true about the equation?\newline(A) The solution is z=1z = -1.\newline(B) There is no solution because 1=11 = -1 is a false equation.\newline(C) There are infinitely many solutions because 1=11 = -1 is a false equation.\newline(D) The solution is (1,1)(1, -1).

Full solution

Q. Matt solved the equation 3(z+1)2=4zz13(z + 1) - 2 = 4z - z - 1. Here are his last two steps:\newline3z+1=3z13z + 1 = 3z - 1\newline1=11 = -1\newlineWhich statement is true about the equation?\newline(A) The solution is z=1z = -1.\newline(B) There is no solution because 1=11 = -1 is a false equation.\newline(C) There are infinitely many solutions because 1=11 = -1 is a false equation.\newline(D) The solution is (1,1)(1, -1).
  1. Simplify left side: Simplify the left side of the equation: 3(z+1)2=3z+32=3z+13(z + 1) - 2 = 3z + 3 - 2 = 3z + 1
  2. Simplify right side: Simplify the right side of the equation: 4zz1=3z14z - z - 1 = 3z - 1
  3. Set equal: Set the simplified left side equal to the simplified right side: 3z+1=3z13z + 1 = 3z - 1
  4. Subtract to isolate: Subtract 3z3z from both sides to isolate the constants:\newline1=11 = -1
  5. Analyze solution: Analyze the equation 1=11 = -1: Since 11 cannot equal 1-1, this indicates a contradiction, meaning there is no solution to the equation.

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