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Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer. -2x+4+3x=x-4

Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer.\newline−2x+4+3x=x−4 -2 x+4+3 x=x-4

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Full solution

Q. Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer.\newline−2x+4+3x=x−4 -2 x+4+3 x=x-4
  1. Simplify left side: Simplify the left side of the equation: −2x+4+3x=x−4-2x + 4 + 3x = x - 4. Combine like terms on the left side: (−2x+3x)+4=1x+4(-2x + 3x) + 4 = 1x + 4.
  2. Combine like terms: Simplify the equation further: 1x+4=x−41x + 4 = x - 4. Subtract xx from both sides to isolate constants: 4=−44 = -4.
  3. Isolate constants: Analyze the result: 4=−44 = -4 is a false statement, indicating no values of xx can satisfy the equation.

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