The image illustrates the general form of a
linear equation in one variable. Let's break it down and explain the components:
General Form:
The linear equation is written as:
\[
Ax + B = 0
\]
Components:
1.
\( A \): This represents the
coefficient of the variable \( x \). It is a constant that multiplies the variable \( x \).
2.
\( x \): This is the
variable in the equation. It is the unknown quantity we are solving for.
3.
\( B \): This is the
constant term. It is a fixed number that does not depend on the variable \( x \).
4.
\( = 0 \): The equation is set equal to zero, which is the standard form for solving linear equations.
Explanation:
A linear equation in one variable is an equation where the highest power of the variable \( x \) is 1. This means the equation forms a straight line when graphed on a coordinate plane.
Steps to Solve:
To solve a linear equation in one variable, follow these steps:
1.
Isolate the Variable Term:
- Move the constant term \( B \) to the other side of the equation by performing the opposite operation (addition or subtraction).
2.
Solve for \( x \):
- Divide both sides of the equation by the coefficient \( A \) to isolate \( x \).
Example:
Let's solve a specific example to illustrate the process:
\[
3x + 5 = 0
\]
#### Step 1: Isolate the Variable Term
Subtract 5 from both sides:
\[
3x + 5 - 5 = 0 - 5
\]
\[
3x = -5
\]
#### Step 2: Solve for \( x \)
Divide both sides by 3:
\[
x = \frac{-5}{3}
\]
So, the solution is:
\[
x = -\frac{5}{3}
\]
Final Answer:
The general form of a linear equation in one variable is:
\[
\boxed{Ax + B = 0}
\]
Parent Tip: Review the logic above to help your child master the concept of linear equation in one variable worksheet.
