Solving Linear Equations in One Variable Quiz

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:

1. Arrange the equation in standard form: If the equation is not already in the standard form, rewrite it in that form.
2. Isolate the variable: Move all constants to one side of the equation and the variable to the other side.
3. Simplify the equation: Perform any necessary operations, such as addition, subtraction, multiplication, or division, to simplify the equation.
4. 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.