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Which statement is true given the two equations?

Equation A:-4-3(1-x)=3x-7
Equation B: 2(x-9)=-2-2(8+x)

Question 15 options:

Equation A has an infinite solution and Equation b has no solution

Only Equation A has an infinite solution

Both equations have no solution

Both equations have an infinite solution

1 answer

To determine the truth of the statements regarding the two equations, let's solve each equation step by step.

Equation A:

\[ -4 - 3(1 - x) = 3x - 7 \]

  1. Distribute -3: \[ -4 - 3 + 3x = 3x - 7 \] This simplifies to: \[ -7 + 3x = 3x - 7 \]

  2. Subtract \(3x\) from both sides: \[ -7 = -7 \] This is a true statement, indicating that Equation A has infinite solutions.

Equation B:

\[ 2(x - 9) = -2 - 2(8 + x) \]

  1. Distribute on both sides: \[ 2x - 18 = -2 - 16 - 2x \] Simplifying the right side gives: \[ 2x - 18 = -18 - 2x \]

  2. Add \(2x\) to both sides: \[ 2x + 2x - 18 = -18 \] Simplifies to: \[ 4x - 18 = -18 \]

  3. Add 18 to both sides: \[ 4x = 0 \]

  4. Divide by 4: \[ x = 0 \] This indicates that Equation B has a unique solution (specifically \(x = 0\)).

Conclusion:

  • Equation A has infinite solutions.
  • Equation B has a unique solution.

From the options given, the correct statement is:

  • Only Equation A has an infinite solution.