Which one of the following is not a linear equation in one variable? (A) 5 + 4x = y + 3 (B) 3t - 1 = 2t + 5 (C) x^2 - 1 = 0 (D) x^2 - x + 1 = 0 (E) x + 2y = y - x
Understand the Problem
The question is asking which of the provided equations is not a linear equation in one variable. We need to identify the equations one by one to determine which one doesn't fit the criteria of linearity.
Answer
The equation that is not a linear equation in one variable is $2x - 1 = x^2$.
Answer for screen readers
The equation that is not a linear equation in one variable is $2x - 1 = x^2$ (Option C).
Steps to Solve
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Identify Linear Equations Linear equations can be expressed in the form $Ax + B = C$, where $A$, $B$, and $C$ are constants, and $x$ is the variable.
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Evaluate Each Option
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Option (A): $2x + 1 = y - 3$
Rearrange to $2x - y + 4 = 0$. This involves two variables ($x$ and $y$), so it is not linear in one variable. -
Option (B): $3t - 1 = 2t + 5$
Rearrange to $t - 6 = 0$, which is a linear equation in one variable. -
Option (C): $2x - 1 = x^2$
This contains $x^2$, which indicates it is quadratic, not linear. -
Option (D): $x^2 - x + 1 = 0$
Again, this involves $x^2$, making it quadratic, not linear.
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Conclusion From the evaluations, Options (A), (C), and (D) involve multiple variables or squared terms. The one not fitting the criterion as a linear equation in one variable would be either (A), (C), or (D).
However, since the question specifically asks for one answer, Option (C) is the most evident due to the presence of the squared term.
The equation that is not a linear equation in one variable is $2x - 1 = x^2$ (Option C).
More Information
Linear equations in one variable have a degree of 1, meaning the highest exponent of the variable is 1. Equations that contain squared variables (degree higher than 1) are classified as polynomial equations or quadratic equations.
Tips
- Confusing linear equations with quadratic equations by not properly recognizing the degree of the variable.
- Misidentifying equations with multiple variables as linear, which they are not.
- Failing to simplify or rearrange equations to see all variables clearly.
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