Math Problem Statement

Make x subject of the formula

Make x the subject of the formula: ax + b = cx + d

Solution

The equation given is:

ax+b=cx+dax + b = cx + d

To solve for xx, follow these steps:

  1. Move all terms involving xx to one side: Subtract cxcx from both sides: axcx+b=dax - cx + b = d

  2. Simplify the terms involving xx: Combine like terms: (ac)x+b=d(a - c)x + b = d

  3. Move constant terms to the other side: Subtract bb from both sides: (ac)x=db(a - c)x = d - b

  4. Solve for xx: Divide both sides by aca - c (assuming aca \neq c): x=dbacx = \frac{d - b}{a - c}

Thus, the formula for xx is:

x=dbacx = \frac{d - b}{a - c}

Let me know if you'd like further clarification or detailed steps for this! Here are five follow-up questions for practice:

  1. What happens if a=ca = c in the original equation?
  2. How can this formula be applied to a specific numerical example?
  3. What is the significance of aca - c in the denominator?
  4. How do you check if your solution for xx is correct?
  5. Can this formula be extended to equations with more variables?

Tip: Always isolate terms involving the variable step by step to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Variable Isolation

Formulas

x = (d - b) / (a - c)

Theorems

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Suitable Grade Level

Grades 8-10