Solve $$ 3 \frac{1}{5}f-\frac{4}{5} $$. Graph the solution set on a number line. Part A Solve the inequality. Complete the inequality. \begin{tabular}{|ll}\hline Clear Show Correct Answer & Check Answer \end{tabular}

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Solve $$ 3 \frac{1}{5}>f-\frac{4}{5} $$. Graph the solution set on a number line. Part A Solve the inequality. Complete the inequality. \begin{tabular}{|ll}\hline Clear Show Correct Answer & Check Answer \end{tabular}

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Sure, let's solve the inequality step by step and then graph the solution on a number line. ### **Given Inequality:** $$ 3 \frac{1}{5} > f - \frac{4}{5} $$ ### **Step 1: Convert Mixed Number to Improper Fraction** First, convert $$ 3 \frac{1}{5} $$ to an improper fraction. $$ 3 \frac{1}{5} = \frac{16}{5} $$ Now, the inequality becomes: $$ \frac{16}{5} > f - \frac{4}{5} $$ ### **Step 2: Isolate the Variable $$ f $$** To solve for $$ f $$, we'll isolate it on one side of the inequality. Start by adding $$ \frac{4}{5} $$ to both sides to eliminate the constant term on the right side. $$ \frac{16}{5} + \frac{4}{5} > f $$ $$ \frac{20}{5} > f $$ ### **Step 3: Simplify the Fraction** Simplify $$ \frac{20}{5} $$: $$ \frac{20}{5} = 4 $$ So, the inequality simplifies to: $$ 4 > f $$ or equivalently, $$ f < 4 $$ ### **Solution:** $$ f < 4 $$ ### **Graphing the Solution on a Number Line:** 1. **Draw a Horizontal Line:** Representing numbers from, say, 0 to 5 for clarity. 2. **Mark the Point $$ 4 $$:** Place a **open circle** at $$ 4 $$ to indicate that $$ 4 $$ is **not included** in the solution. 3. **Shade to the Left of $$ 4 $$:** Since $$ f $$ is less than $$ 4 $$, shade all numbers to the left of $$ 4 $$. #### **Number Line Representation:** ``` <---|-----|-----|-----|-----|-----|---> 0 1 2 3 4 5 o========> ``` - **Open Circle (o)** at $$ 4 $$: Indicates $$ 4 $$ is not included. - **Arrow/Line to the Left of $$ 4 $$**: Represents all real numbers less than $$ 4 $$. This graphical representation shows all the possible values of $$ f $$ that satisfy the inequality $$ f < 4 $$. $$ f < 4 $$ To graph the solution on a number line: - Draw a horizontal line from 0 to 5. - Place an open circle at 4. - Shade all numbers to the left of 4. This shows that $$ f $$ can be any number less than 4.

Solve . Graph the solution set on a number line.
Part A Solve the inequality.
Complete the inequality.

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Solve . Graph the solution set on a number line. Part A Solve the inequality. Complete the inequality. Clear Show Correct Answer Check Answer