Simplify 2whole one fifth p minus 7 greater than 4

To simplify the inequality \(2\frac{1}{5}p - 7 > 4\), let's break it down step by step.

### Step 1: Convert the mixed number to an improper fraction
First, convert \(2\frac{1}{5}\) into an improper fraction.

\[
2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}
\]

So, the inequality becomes:

\[
\frac{11}{5}p - 7 > 4
\]

### Step 2: Isolate the term with \( p \)
Add 7 to both sides of the inequality to isolate the term involving \( p \):

\[
\frac{11}{5}p > 4 + 7
\]

\[
\frac{11}{5}p > 11
\]

### Step 3: Solve for \( p \)
To solve for \( p \), multiply both sides of the inequality by the reciprocal of \(\frac{11}{5}\), which is \(\frac{5}{11}\):

\[
p > 11 \times \frac{5}{11}
\]

\[
p > 5
\]

So, the simplified solution is:

\[
p > 5
\]

Would you like more details or have any questions? Here are some related questions:

1. What would the solution be if the inequality was \( \leq \) instead of \( > \)?
2. How would the solution change if the inequality was \(2\frac{1}{5}p - 7 \geq 4\)?
3. What if the inequality was \(3p - 7 > 4\)?
4. How do you graph the solution \(p > 5\) on a number line?
5. How do you solve the inequality if the coefficient of \(p\) was a negative fraction?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to simplify the inequality 2 1/5p - 7 > 4 step-by-step. This problem involves converting mixed numbers to improper fractions and solving linear inequalities. Suitable for students in Grades 6-8.

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