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 = \boxed{\phantom{0}}[/tex]



Answer :

To solve the equation [tex]\(\frac{p+1}{2} = \frac{3p+7}{5}\)[/tex], we will go through the following steps:

1. Eliminate the fractions by finding a common multiple of the denominators (2 and 5), which is 10. Multiply both sides of the equation by 10 to clear the denominators.

[tex]\[ 10 \cdot \frac{p+1}{2} = 10 \cdot \frac{3p+7}{5} \][/tex]

2. Simplify the equation after multiplying:

[tex]\[ 5(p+1) = 2(3p+7) \][/tex]

3. Distribute the numbers on both sides of the equation:

[tex]\[ 5p + 5 = 6p + 14 \][/tex]

4. To isolate [tex]\(p\)[/tex], move all the [tex]\(p\)[/tex]-terms to one side and the constant terms to the other side. Start by subtracting [tex]\(5p\)[/tex] from both sides:

[tex]\[ 5p + 5 - 5p = 6p + 14 - 5p \][/tex]

Simplifying this, we get:

[tex]\[ 5 = p + 14 \][/tex]

5. Next, subtract 14 from both sides to solve for [tex]\(p\)[/tex]:

[tex]\[ 5 - 14 = p + 14 - 14 \][/tex]

Simplifying this, we get:

[tex]\[ -9 = p \][/tex]

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

[tex]\[ p = -9 \][/tex]