The inequality you provided is:

\[
0.33x + 0.52y \leq 5
\]

This is a linear inequality with two variables, \(x\) and \(y\). To find the possible values of \(x\) and \(y\), you can interpret this as the region on a coordinate plane that satisfies the inequality. Here's how you can proceed:

### Step 1: Solve for \(y\)
We can isolate \(y\) to express the inequality in slope-intercept form (\(y = mx + b\)).

\[
0.52y \leq 5 - 0.33x
\]

\[
y \leq \frac{5 - 0.33x}{0.52}
\]

Simplify:

\[
y \leq \frac{5}{0.52} - \frac{0.33}{0.52}x
\]

\[
y \leq 9.62 - 0.635x
\]

### Step 2: Interpret the result
The inequality \(y \leq 9.62 - 0.635x\) represents a line on the coordinate plane with slope \(-0.635\) and a y-intercept at \(9.62\). The region below this line (since it’s \(\leq\)) will contain all the possible solutions for \(x\) and \(y\).

### Step 3: Graphical representation
The set of all points \((x, y)\) that satisfy the inequality is the shaded region below the line.

#### Sample solutions
You can substitute specific values of \(x\) to get corresponding \(y\) values:

- If \(x = 0\):
  \[
  y \leq 9.62
  \]
- If \(x = 10\):
  \[
  y \leq 3.27
  \]

Thus, any pair \((x, y)\) satisfying these conditions will be a solution.

Would you like to see a graph or explore more details?

### Related Questions:
1. What is the slope and intercept of the line represented by the equation?
2. How would you solve the inequality if \(x\) or \(y\) had a specific value?
3. What is the graphical representation of this inequality?
4. How do you handle systems of inequalities?
5. What is the difference between linear equations and linear inequalities?

**Tip:** Always check the boundary line by setting the inequality as an equality (i.e., \(0.33x + 0.52y = 5\)) for better understanding of the region.

Discover how to solve the linear inequality 0.33x + 0.52y ≤ 5 by expressing the inequality in slope-intercept form. Learn key algebraic concepts and find possible values for x and y. Suitable for students in Grades 9-11.

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