Math Problem Statement

Which of these equations is a linear equation in one variable? Options: (i) 2x + 5 = 14x (ii) 2x + 5y = 14 (iii) 2x^2 + 5 = 4 (iv) 2/x + 3x = 0

Solution

The question asks which of the given equations is a linear equation in one variable.

Let's examine each option:

  1. 2x+5=14x2x + 5 = 14x
    This is a linear equation because it can be written as 2x14x=52x - 14x = -5 or 12x=5-12x = -5, which is in the form ax+b=0ax + b = 0, representing a linear equation in one variable xx.

  2. 2x+5y=142x + 5y = 14
    This equation involves two variables, xx and yy, so it is not a linear equation in one variable.

  3. 2x2+5=42x^2 + 5 = 4
    This is a quadratic equation because it contains x2x^2, meaning it is not linear.

  4. 2x+3x=0\frac{2}{x} + 3x = 0
    This is not linear because 2x\frac{2}{x} is not a linear term. It contains a variable in the denominator.

Conclusion:

The correct answer is (i) 2x+5=14x2x + 5 = 14x,** which is the linear equation in one variable.

Would you like more details on how to solve these types of equations, or do you have any questions?

Here are some related questions to consider:

  1. How do you solve linear equations in one variable?
  2. What makes an equation quadratic instead of linear?
  3. Can linear equations have more than one variable?
  4. How do you handle equations with variables in the denominator?
  5. What are the general forms of linear and quadratic equations?

Tip: Always check for powers of the variable or multiple variables to determine if an equation is linear.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Variables

Formulas

Linear equation form: ax + b = 0

Theorems

Definition of linear equations

Suitable Grade Level

Grade 8