Math Problem Statement

The image shows some math problems involving fractions and equations where the user attempts to solve for x, but the solutions seem to be incorrect as marked with '×'.

Solution

The image shows some math problems involving fractions and equations. The equations appear to involve solving for xx, but the mathematical steps leading to the solution are incorrect as they are marked with "×".

Let's analyze the first problem and the likely intention of the question:

Equation 1 (Top left corner):

36x=2412\frac{36}{x} = \frac{24}{12}

To solve for xx, cross-multiply: 3612=24x36 \cdot 12 = 24 \cdot x

This simplifies to: 432=24x432 = 24x

Now, solve for xx: x=43224=18x = \frac{432}{24} = 18

Equation 2 (Middle top):

3612=x24\frac{36}{12} = \frac{x}{24}

Cross-multiply: 3624=12x36 \cdot 24 = 12 \cdot x

This simplifies to: 864=12x864 = 12x

Now, solve for xx: x=86412=72x = \frac{864}{12} = 72

Equation 3 (Top right):

24x=3612\frac{24}{x} = \frac{36}{12}

Cross-multiply: 2412=36x24 \cdot 12 = 36 \cdot x

This simplifies to: 288=36x288 = 36x

Solve for xx: x=28836=8x = \frac{288}{36} = 8

The remaining set of equations follows a similar structure but appears to be a repetition of the above methods. It seems the problems may have been solved incorrectly in the image, as shown by the "×" marks.

Would you like me to analyze the other set of equations further? Let me know if you'd like additional details.


Here are 5 related questions to further explore the concept:

  1. How do you cross-multiply two fractions?
  2. Can you explain why dividing by zero is undefined?
  3. How do you solve proportions involving fractions?
  4. How can you check if your solution to a proportion is correct?
  5. How do ratios and proportions apply to real-world problems?

Tip: Always simplify fractions where possible before cross-multiplying to make calculations easier.

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Math Problem Analysis

Mathematical Concepts

Fractions
Proportions
Algebra

Formulas

Cross-multiplication: a/b = c/d → a * d = b * c
Solving for x in proportions: cross-multiply and solve

Theorems

Proportion theorem: If a/b = c/d, then ad = bc

Suitable Grade Level

Grades 6-8