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Solve for p p .\newline2p+15p+6=17p=□\frac{2p+1}{5p+6}=\frac{1}{7}\\[1ex]p=\square

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Full solution

Q. Solve for p p .\newline2p+15p+6=17p=□\frac{2p+1}{5p+6}=\frac{1}{7}\\[1ex]p=\square
  1. Set up equation: Set up the equation from the problem.\newlineWe have the equation (2p+1)/(5p+6)=1/7(2p+1)/(5p+6) = 1/7. We need to solve for pp.
  2. Cross-multiply: Cross-multiply to eliminate the fractions.\newlineCross-multiplying gives us 7(2p+1)=1(5p+6)7(2p+1) = 1(5p+6).
  3. Distribute numbers: Distribute the numbers on both sides of the equation.\newlineThis gives us 14p+7=5p+614p + 7 = 5p + 6.
  4. Move terms: Move all terms containing pp to one side and constant terms to the other side.\newlineSubtract 5p5p from both sides to get 14p−5p+7=614p - 5p + 7 = 6.\newlineSubtract 77 from both sides to get 14p−5p=6−714p - 5p = 6 - 7.
  5. Simplify equation: Simplify both sides of the equation.\newlineThis gives us 9p=−19p = -1.
  6. Solve for pp: Solve for pp by dividing both sides by 99.\newlineDividing by 99 gives us p=−19p = -\frac{1}{9}.

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