Math Problem Statement

Find the unknown term in the proportion: (2x + 3) / 5 = 7 / 10.

Solution

The image shows a proportion equation in Ukrainian, which translates to "Find the unknown term in the proportion." The equation is:

2x+35=710\frac{2x + 3}{5} = \frac{7}{10}

To solve for xx, follow these steps:

  1. Cross-multiply the two ratios: (2x+3)10=57(2x + 3) \cdot 10 = 5 \cdot 7 10(2x+3)=3510(2x + 3) = 35

  2. Distribute the 10 on the left-hand side: 20x+30=3520x + 30 = 35

  3. Subtract 30 from both sides to isolate the term with xx: 20x=520x = 5

  4. Divide by 20 to solve for xx: x=520=0.25x = \frac{5}{20} = 0.25

Thus, the value of xx is 0.250.25.

Do you need more details or have any questions?

Here are five related questions to expand your understanding:

  1. How would the solution change if the proportion was 2x+55=710\frac{2x + 5}{5} = \frac{7}{10}?
  2. What happens if the proportion is inverted, such as 52x+3=107\frac{5}{2x+3} = \frac{10}{7}?
  3. How can proportions be applied in real-life scenarios, such as in cooking or finance?
  4. Can you solve proportions where both the numerator and denominator are polynomials?
  5. How do proportions relate to the concept of similar triangles in geometry?

Tip: Cross-multiplication is a powerful tool to solve proportions quickly and efficiently!

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Math Problem Analysis

Mathematical Concepts

Algebra
Proportions
Linear Equations

Formulas

Cross-multiplication
Solving linear equations

Theorems

Cross-multiplication in proportions

Suitable Grade Level

Grades 6-8