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How many solutions does this equation have?\newline5p=8+5p5p = 8 + 5p\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Find the number of solutions to a linear equationright chevron icon

Full solution

Q. How many solutions does this equation have?\newline5p=8+5p5p = 8 + 5p\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Equation: Analyze the equation 5p=8+5p5p = 8 + 5p. We want to find out how many values of pp satisfy this equation.
  2. Subtract to Isolate pp: Subtract 5p5p from both sides of the equation to try to isolate pp.5p−5p=8+5p−5p5p - 5p = 8 + 5p - 5p
  3. Simplify After Subtraction: Simplify both sides of the equation after subtraction.\newline0=80 = 8
  4. Determine Truth Value: Determine the truth value of the simplified equation.\newline0=80 = 8 is never true for any value of pp, which means there is no value of pp that can satisfy the equation.
  5. Conclude Number of Solutions: Conclude the number of solutions based on the previous step.\newlineSince the equation 0=80 = 8 is false, the original equation 5p=8+5p5p = 8 + 5p has no solution.

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