Final answer:
To find the value of p in the inequality 4/5p + 9 > 6, subtract 9 from both sides and then multiply by 5/4 to isolate p, yielding p > -15/4 or -3.75.
Step-by-step explanation:
The value of p in the inequality 4/5p + 9 > 6 can be found by first isolating the term containing p on one side of the inequality. Here is a step-by-step solution:
- Subtract 9 from both sides of the inequality: 4/5p + 9 - 9 > 6 - 9, which simplifies to 4/5p > -3.
- Multiply both sides by 5/4 to get p on its own: (5/4)(4/5)p > (5/4)(-3), which simplifies to p > -15/4.
Therefore, the value of p must be greater than -15/4 or -3.75 to satisfy the inequality.