Math Problem Statement

12y ≤ 0.10x

Solution

The inequality provided in the image is:

12y0.10x12y \leq 0.10x

Steps to Analyze or Solve

  1. Rearranging the inequality: To understand its behavior better, you can express yy in terms of xx by dividing through by 12: y0.10x12y \leq \frac{0.10x}{12}

  2. Simplify the fraction: yx120y \leq \frac{x}{120}

This is the simplified version of the inequality.

Graphical Representation

This inequality represents a region in the coordinate plane:

  • The boundary line is y=x120y = \frac{x}{120}.
  • The solution region includes all points (x,y)(x, y) where yy is less than or equal to x120\frac{x}{120}.

Would you like further explanation, or should we explore this inequality graphically or through examples?

Related Questions

  1. What does the slope 1120\frac{1}{120} indicate in the inequality yx120y \leq \frac{x}{120}?
  2. How can we test whether a specific point, like (12, 1), satisfies the inequality?
  3. What is the significance of dividing both sides of an inequality in terms of scaling the boundary?
  4. How would this inequality change if the \leq sign were reversed to \geq?
  5. How do we interpret such inequalities in practical scenarios?

Tip:

When graphing inequalities, always remember to shade the correct side of the boundary line, depending on whether it's \leq or \geq.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Linear Equations

Formulas

y ≤ (0.10/12)x
y ≤ x/120

Theorems

Linear inequality properties

Suitable Grade Level

Grades 7-9