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Solve the following equation. Then place the correct number in the box provided. Leave the answer in terms of a mixed number.

6(2p - 1) > 5p

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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.

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