IndietroIdentifying and Solving Linear Equations in One Variable
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Q1. Which of the following is a linear equation in one variable?
Background
Topic: Linear Equations in One Variable
This question tests your ability to recognize linear equations in one variable. A linear equation in one variable is an equation that can be written in the form , where is the variable and , , and are constants.
Key Terms and Formulas:
Linear Equation: An equation where the variable is raised only to the first power and appears in no denominators, exponents, or radicals.
One Variable: The equation contains only one variable (e.g., ).
Standard Form:
Step-by-Step Guidance
Examine each option and identify the variable(s) present in the equation or expression.
Check if the equation can be written in the form (where , , and are constants and is the only variable).
Ensure that the variable is not raised to any power other than 1, is not inside a radical, and does not appear in the denominator.
Eliminate any options that are not equations (i.e., expressions without an equals sign) or that have more than one variable or a variable with an exponent other than 1.
For the remaining options, confirm that they are equations in one variable and are linear.
Try solving on your own before revealing the answer!
Final Answer:
The correct answer is the option that matches the form and contains only one variable raised to the first power. For example, is a linear equation in one variable.
Other options may be expressions (not equations), have more than one variable, or have variables with exponents other than 1.
