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Solve this equation for [tex]\( p \)[/tex]:

[tex]\[
\frac{p+1}{2} = \frac{3p+7}{5}
\][/tex]

Type the correct answer in the box. Use numerals instead of words.

[tex]\[
p = \quad \boxed{}
\][/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(\frac{p+1}{2} = \frac{3p+7}{5}\)[/tex] for [tex]\(p\)[/tex], follow these steps:

1. Eliminate the fractions by cross-multiplying:
[tex]\[ 5 \cdot (p + 1) = 2 \cdot (3p + 7) \][/tex]

2. Distribute on both sides:
[tex]\[ 5p + 5 = 6p + 14 \][/tex]

3. Move all terms involving [tex]\(p\)[/tex] to one side and constants to the other side:
[tex]\[ 5p - 6p = 14 - 5 \][/tex]

4. Simplify the equation:
[tex]\[ -p = 9 \][/tex]

5. Solve for [tex]\(p\)[/tex] by dividing both sides by [tex]\(-1\)[/tex]:
[tex]\[ p = -9 \][/tex]

Thus, the solution to the equation [tex]\(\frac{p+1}{2} = \frac{3p+7}{5}\)[/tex] is:
[tex]\[ p = -9 \][/tex]
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