Respuesta :

Sprnt

Answer:

[tex]p=\frac{5}{24}[/tex].

Step-by-step explanation:

1. Write the expression.

[tex]-\frac{2}{3p} +\frac{1}{5} -1+\frac{5}{6p}[/tex]

2. Equal the expression to 0.

[tex]-\frac{2}{3p} +\frac{1}{5} -1+\frac{5}{6p}=0[/tex]

3. Substract [tex]\frac{1}{5}[/tex] from both sides.

[tex]-\frac{2}{3p} +\frac{1}{5} -1+\frac{5}{6p}-\frac{1}{5} =-\frac{1}{5} \\ \\-\frac{2}{3p} } -1+\frac{5}{6p}=-\frac{1}{5}[/tex]

4. Add 1 to both sides.

[tex]-\frac{2}{3p} } -1+\frac{5}{6p}+1=-\frac{1}{5}+1\\ \\-\frac{2}{3p} } +\frac{5}{6p}=-\frac{1}{5}+1\\ \\-\frac{2}{3p} } +\frac{5}{6p}=-\frac{1}{5}+\frac{5}{5} \\ \\-\frac{2}{3p} } +\frac{5}{6p}=\frac{4}{5}[/tex]

5. Simplify the left side by solvind the addition, factorize 1/p.

[tex]\frac{1}{p} (-\frac{2}{3} } +\frac{5}{6})=\frac{4}{5} \\ \\\frac{1}{p} (\frac{1}{6})=\frac{4}{5}[/tex]

6. Multiply by the reciprocal of 1/6 (6).

[tex]\frac{1}{p} (\frac{1}{6})*6=\frac{4}{5}*6 \\ \\\frac{1}{p}=\frac{24}{5}[/tex]

7. Inverse both sides of the equation.

[tex]p=\frac{5}{24}[/tex]

8. Express your result.

[tex]p=\frac{5}{24}[/tex].

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