Answer:
The value of p is -8
Explanation:
Given:
[tex]\frac{1}{2}p\text{ + 7 = }\frac{3}{4}p\text{ + 9}[/tex]
To find:
the value of p
To determine p, we will collect like terms and then simplify:
[tex]\begin{gathered} subtract\text{ }\frac{3}{4}p\text{ from both sides:} \\ \frac{1}{2}p\text{ - }\frac{3}{4}p\text{ + 7 = }\frac{3}{4}p\text{ - }\frac{3}{4}p\text{ + 9} \\ \\ \frac{2p\text{ - 3p}}{4}\text{ + 7 = 0 + 9} \end{gathered}[/tex][tex]\begin{gathered} \frac{-p}{4}\text{ + 7 = 9} \\ \\ subtract\text{ 7 from both sides:} \\ \frac{-p}{4}\text{ + 7 - 7 = 9 - 7} \\ \\ \frac{-p}{4}\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} Multiply\text{ both sides by 4:} \\ \frac{-4p}{4}\text{ = 2\lparen4\rparen} \\ \\ -p\text{ = 8 } \\ \\ p\text{ = -8} \end{gathered}[/tex]
