4. The cost of a product to a retailer is $$ \$ 3.40 $$. If the retailer wishes to make a profit of $$ 20 \% $$ on the selling price, at what price should the product be sold? 5. Solve the following inequalities and represent your answer on a real number-line and in interval form. (a) $$ 5 x-11 \leq 9 $$

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**Problem 4**

We let the selling price be $$ S $$. The retailer makes a profit of $$ 20\% $$ on the selling price, meaning that the profit is 
$$
0.20 S.
$$
Also, the profit is the difference between the selling price and the cost, so
$$
S - 3.40 = 0.20 S.
$$
To solve for $$ S $$, subtract $$ 0.20S $$ from both sides:
$$
S - 0.20S - 3.40 = 0.
$$
This simplifies to:
$$
0.80 S = 3.40.
$$
Now, divide both sides by $$ 0.80 $$:
$$
S = \frac{3.40}{0.80} = 4.25.
$$
Thus, the product should be sold for $$\$4.25$$.

---

**Problem 5(a)**

We start with the inequality:
$$
5x - 11 \leq 9.
$$
First, add $$ 11 $$ to both sides:
$$
5x \leq 9 + 11,
$$
which simplifies to:
$$
5x \leq 20.
$$
Next, divide both sides by $$ 5 $$:
$$
x \leq \frac{20}{5} = 4.
$$

**Representation on a number line:**

- Draw a number line.
- Mark the point $$ x = 4 $$ with a closed circle (since $$ x = 4 $$ is included).
- Shade the region to the left of $$ 4 $$ to represent all values $$ x \leq 4 $$.

**Interval form:** $$(-\infty, 4]$$.
**Problem 4** The retailer should sell the product for \$4.25 to make a 20% profit. --- **Problem 5(a)** Solve the inequality $$ 5x - 11 \leq 9 $$: 1. Add 11 to both sides: $$ 5x \leq 20 $$ 2. Divide both sides by 5: $$ x \leq 4 $$ **Number Line Representation:** - Draw a number line. - Mark $$ x = 4 $$ with a closed circle. - Shade all values to the left of 4. **Interval Form:** $$(-\infty, 4]$$.

The cost of a product to a retailer is . If the retailer wishes to make a profit of on the selling
price, at what price should the product be sold?

Solve the following inequalities and represent your answer on a real number-line and in interval form.
(a)

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The cost of a product to a retailer is . If the retailer wishes to make a profit of on the selling price, at what price should the product be sold? Solve the following inequalities and represent your answer on a real number-line and in interval form. (a)