Math Problem Statement

Solve the equations extracted from the image.

Solution

Let me analyze the content of the image for mathematical equations. I will extract and solve the equations shown in the photo. One moment please.The image contains various equations. Here is the extraction and solving process for the visible equations:

  1. Equation: 5x+2x7x=x5x + 2x - 7x = x

    • Combine like terms on the left-hand side: 5x+2x7x=05x + 2x - 7x = 0
    • The equation becomes: 0=x0 = x
    • Solution: x=0x = 0.
  2. Equation: 5(x2)=x5(x - 2) = x

    • Expand the left-hand side: 5x10=x5x - 10 = x
    • Subtract xx from both sides: 4x10=04x - 10 = 0
    • Add 10 to both sides: 4x=104x = 10
    • Divide by 4: x=104=52x = \frac{10}{4} = \frac{5}{2}
    • Solution: x=52x = \frac{5}{2}.
  3. Equation: x+x=xx + x = x

    • Combine terms on the left-hand side: 2x=x2x = x
    • Subtract xx from both sides: x=0x = 0
    • Solution: x=0x = 0.
  4. Equation: x+4=4xx + 4 = 4 - x

    • Add xx to both sides: 2x+4=42x + 4 = 4
    • Subtract 4 from both sides: 2x=02x = 0
    • Divide by 2: x=0x = 0
    • Solution: x=0x = 0.

If there are additional equations you'd like analyzed, feel free to point them out or upload another photo!


Would you like details on any specific step or additional help? Here are 5 related questions you might explore next:

  1. How can we verify these solutions graphically?
  2. What types of equations lead to no solution or infinite solutions?
  3. How do we approach equations with fractions differently?
  4. What is the meaning of a solution like x=0x = 0 in real-world applications?
  5. How do equations with variables on both sides differ from simpler ones?

Tip: Always simplify each side of the equation first before moving terms across the equal sign!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Equation Solving

Formulas

Basic equation simplification and balancing

Theorems

Properties of Equality

Suitable Grade Level

Grades 6-8