15 Questions
What is the standard form of a linear equation in one variable?
$ax + b = 0$
What is the degree of the variable in a linear equation?
1
How many possible solutions does a linear equation in one variable have?
One
What are the steps to solve a linear equation in one variable?
Arrange in standard form, isolate the variable, simplify the equation, find the solution
How should the solution for the variable be written?
x = c
Solve the equation $5x - 9 = -3x + 19$.
$x = 4$
What are the applications of linear equations in one variable in real-life situations?
Representing conditions dependent on one variable, modeling relationships between variables, and solving problems involving unknown values.
Why are linear equations in one variable considered essential tools in mathematics?
They provide a simple and straightforward way to represent and solve problems involving a single variable.
What are the steps to solve the equation $10 - 3x = 7$?
First, subtract 7 from both sides, then add 3x to both sides, and finally divide by 3 to find the solution.
In the equation $2x + 3 = 8$, what is the solution for x?
$x = 5/2$ or $x = 2.5$
What is the solution to the equation $2x + 3 = 8$?
$x = 5/2$
How can linear equations in one variable be applied in real-life situations?
They can be used to represent conditions dependent on one variable, model relationships between variables, and solve problems involving unknown values.
In the equation $5x - 9 = -3x + 19$, what is the solution for $x$?
$x = 4$
What are the essential steps to solve the linear equation $10 - 3x = 7$?
Subtract 7 from both sides, then divide by -3 to find the value of $x$.
Why are linear equations in one variable important in mathematics?
They provide a simple and straightforward way to represent and solve problems involving a single variable.
Study Notes
Equations in One Variable:Linear Equations
A linear equation in one variable is an algebraic equation of equality that involves only one variable, with the greatest exponent of that variable being 1. These equations are represented in the form of $$ax + b = 0$$, where $$a$$ and $$b$$ are integers, and $$x$$ is the variable with only one solution. Some key aspects of linear equations in one variable include:
- Degree: The degree of the variable in a linear equation is 1.
- Standard Form: The standard form of a linear equation in one variable is $$ax + b = 0$$.
- Solution: Linear equations in one variable have only one possible solution for the value of the variable.
Solving Linear Equations in One Variable
To solve a linear equation in one variable, follow these steps:
- Arrange the equation in standard form: If the equation is not already in the standard form, rewrite it in that form.
- Isolate the variable: Move all constants to one side of the equation and the variable to the other side.
- Simplify the equation: Perform any necessary operations, such as addition, subtraction, multiplication, or division, to simplify the equation.
- Find the solution: Solve for the variable and write the answer in the form "x = c", where $$c$$ is the constant term.
Examples of Linear Equations in One Variable
Here are some examples of linear equations in one variable:
- $$2x + 3 = 8$$
- $$5x - 9 = -3x + 19$$
- $$10 - 3x = 7$$
To solve these equations, follow the steps mentioned above. For instance, in the first example, $$2x + 3 = 8$$, isolate the variable by moving the constant term to the left side: $$2x = 8 - 3$$. Then, simplify by subtracting 8 from both sides: $$2x = -5$$. Finally, divide by 2 to find the solution: $$x = -5 / 2$$.
Applications of Linear Equations in One Variable
Linear equations in one variable have various applications in real-life situations, such as:
- Representing conditions dependent on one variable
- Modeling relationships between variables
- Solving problems involving unknown values
In conclusion, linear equations in one variable are essential tools in mathematics and have numerous applications in real-life situations. They provide a simple and straightforward way to represent and solve problems involving a single variable.
Test your understanding of linear equations in one variable by taking this quiz. Explore the concept of standard form, the process of isolating the variable, and solving for the solution. Also, learn about real-life applications of linear equations in one variable.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free