Math Problem Statement

Solve the given set of linear equations.

Solution

I see you uploaded a math worksheet image. Let me extract the text from the image and solve the equations. One moment, please. PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/173695479236290qf0wmt.jpg" image = Image.open(image_path)

Use OCR to extract text

extracted_text = pytesseract.image_to_string(image) extracted_textHere is the extracted text from the image, cleaned and formatted for clarity:

Solve:

  1. 10x+5.1=46.110x + 5.1 = 46.1
  2. 4.6x+5.5=50.124.6x + 5.5 = 50.12
  3. 9.6x+18.9=50.589.6x + 18.9 = 50.58
  4. 2.4x+1=7.242.4x + 1 = 7.24
  5. 5.4x+12.7=45.645.4x + 12.7 = 45.64
  6. 2.9x+5=11.672.9x + 5 = 11.67
  7. 4x+4.5=32.14x + 4.5 = 32.1
  8. 9.9x+5.7=54.219.9x + 5.7 = 54.21
  9. 4.3x+8.7=34.074.3x + 8.7 = 34.07
  10. 4.9x+7.1=31.64.9x + 7.1 = 31.6

Let me now solve each equation for xx. sympy import symbols, Eq, solve

Define the variable

x = symbols('x')

List of equations

equations = [ Eq(10x + 5.1, 46.1), Eq(4.6x + 5.5, 50.12), Eq(9.6x + 18.9, 50.58), Eq(2.4x + 1, 7.24), Eq(5.4x + 12.7, 45.64), Eq(2.9x + 5, 11.67), Eq(4x + 4.5, 32.1), Eq(9.9x + 5.7, 54.21), Eq(4.3x + 8.7, 34.07), Eq(4.9x + 7.1, 31.6), ]

Solve each equation

solutions = [solve(eq, x)[0] for eq in equations] solutionsHere are the solutions for each equation:

  1. x=4.1x = 4.1
  2. x=9.7x = 9.7
  3. x=3.3x = 3.3
  4. x=2.6x = 2.6
  5. x=6.1x = 6.1
  6. x=2.3x = 2.3
  7. x=6.9x = 6.9
  8. x=4.9x = 4.9
  9. x=5.9x = 5.9
  10. x=5.0x = 5.0

Would you like detailed step-by-step explanations for solving any specific equation? Let me know!

Related Questions:

  1. How do you isolate xx in linear equations like these?
  2. Can these equations be solved graphically, and if so, how?
  3. What are real-world applications of solving equations like these?
  4. How does changing coefficients or constants affect the solution?
  5. Can you solve systems of linear equations with similar methods?

Tip:

Always double-check your calculations by substituting the solution back into the original equation to verify!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

General form of a linear equation: ax + b = c

Theorems

Basic algebraic principles for solving equations

Suitable Grade Level

Grades 7-9