Final answer:
To solve the inequality 6(2p - 1) > 5p, we first expand and simplify the algebra, then isolate the variable p. After simplifying, we find that the solution to the inequality is p > 6/7, which is reasonable and left as an improper fraction since it cannot be a mixed number.
Step-by-step explanation:
To solve the inequality 6(2p - 1) > 5p, begin by expanding the left side to get 12p - 6 > 5p. Next, we want to eliminate terms to simplify the algebra by moving all terms involving p to one side and constant terms to the other side.
Subtract 5p from both sides: 12p - 5p - 6 > 0 which simplifies to 7p - 6 > 0.
Now, add 6 to both sides: 7p - 6 + 6 > 0 + 6 which simplifies to 7p > 6.
Next, divide both sides by 7 to find the p value: p > 6/7. Since 6/7 is a fraction, we leave the answer as a mixed number, which in this case is simply the improper fraction as it is, since it cannot be converted to a mixed number.
Lastly, check the answer to see if it is reasonable: p > 6/7 makes sense as it represents all numbers greater than 6/7.