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Which of these equations has no solutions?\newlineChoices:\newline(A) 14(12x+16)=5x+4−2x\frac{1}{4}(12x + 16) = 5x + 4 - 2x\newline(B) 3x+1−5x=4x−113x + 1 - 5x = 4x - 11\newline(C) 4(2x−1)=8x−14(2x - 1) = 8x - 1\newlineWhich statement explains a way you can tell the equation has no solutions?\newlineChoices:\newline(A) It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign.\newline(B) It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.\newline(C) It is equivalent to an equation that has different variable terms on either side of the equation.

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Full solution

Q. Which of these equations has no solutions?\newlineChoices:\newline(A) 14(12x+16)=5x+4−2x\frac{1}{4}(12x + 16) = 5x + 4 - 2x\newline(B) 3x+1−5x=4x−113x + 1 - 5x = 4x - 11\newline(C) 4(2x−1)=8x−14(2x - 1) = 8x - 1\newlineWhich statement explains a way you can tell the equation has no solutions?\newlineChoices:\newline(A) It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign.\newline(B) It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.\newline(C) It is equivalent to an equation that has different variable terms on either side of the equation.
  1. Simplify Equation (A): Simplify equation (A) 14(12x+16)=5x+4−2x\frac{1}{4}(12x + 16) = 5x + 4 - 2x; distribute and combine like terms.
  2. Check Equation (A): Check if equation (A) simplifies to a true statement or a contradiction.
  3. Simplify Equation (B): Simplify equation (B) 3x+1−5x=4x−113x + 1 - 5x = 4x - 11; combine like terms.
  4. Rearrange Equation (B): Move all variable terms to one side and constant terms to the other side in equation (B).
  5. Solve for xx: Solve for xx in equation (B).
  6. Simplify Equation (C): Simplify equation (C) 4(2x−1)=8x−14(2x - 1) = 8x - 1; distribute and simplify.
  7. Check Equation (C)(C): Check if equation (C)(C) simplifies to a true statement or a contradiction.

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