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Questions and Answers
Which of the following is a linear equation in one variable?
Which of the following is a linear equation in one variable?
- $\sqrt{x} + 2 = 9$
- $2x^2 + 3x - 5 = 0$
- $\sin(x) = 0$
- $\frac{x}{2} - 3 = 7$ (correct)
Which of the following equations is not a linear equation in one variable?
Which of the following equations is not a linear equation in one variable?
- $4x^2 - 9 = 0$ (correct)
- $\log(x) = 2$
- $\frac{2x}{3} - 1 = 0$
- $3x + 2y = 5$
Which of the following is a solution to the equation $2x - 5 = 7$?
Which of the following is a solution to the equation $2x - 5 = 7$?
- $x = 3$
- $x = -1$ (correct)
- $x = 0$
- $x = 1$
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Study Notes
Identifying Linear Equations
- A linear equation in one variable is characterized by its simplicity and single variable.
- The equation must have a degree of one, meaning the highest power of the variable is one.
Non-Linear Equations
- An equation that does not meet the criteria for a linear equation is considered non-linear.
Solving Equations
- To solve the equation $2x - 5 = 7$, we need to isolate the variable $x$.
- Adding $5$ to both sides gives $2x = 12$, and then dividing both sides by $2$ gives $x = 6$.
- Therefore, the solution to the equation $2x - 5 = 7$ is $x = 6$.
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