Solve the inequality \(\frac{7}{3}<\frac{p}{3}\)

Question

Solve the inequality \(\dfrac{7}{3}<\dfrac{p}{3}\)

Answer 1

Step 1. Swap sides
\[
\frac{7}{3}<\frac{p}{3}
\]
Swap sides:
\[
\frac{p}{3}>\frac{7}{3}
\]

Step 2. Isolate the \(p\)
\[
\frac{p}{3}>\frac{7}{3}
\]
Multiply to both sides by 3 :
\[
\frac{p}{3} \cdot 3>\frac{7}{3} \cdot 3
\]
Group like terms:
\[
\frac{1}{3} \cdot 3 p>\frac{7}{3} \cdot 3
\]
Simplify the fraction:
\[
p>\frac{7}{3} \cdot 3
\]
Multiply the fractions:
\[
p>\frac{7 \cdot 3}{3}
\]
Simplify the right side:
\[
p>7
\]

Step 3. Solution on a coordinate plane

Solution:
\(p>7\)
Interval notation:
\((7, \infty)\)