This document discusses linear equations in one variable. It defines expressions and equations, identifies one-variable linear equations, and explains how to simplify and solve one-variable linear equations. Specifically, it provides examples of algebraic expressions and equations, defines linear equations as having the highest power of the variable being 1, and demonstrates how to isolate the variable on one side of the equation and solve for its value using addition, subtraction, multiplication, or division.

1. Linear Equations in
One Variable
Satyajeet Parida

2. Objectives and Outcomes
• Objective:
To explain about
Expressions, Equations, Linear Equations and solving one variable
linear equations.
• Outcomes:
Student will be able to,
Differentiate between expressions and equations
Identify One variable linear equations
Simplify and solve one variable linear equations

3. Algebraic Expressions
• Some examples of expressions are:
5x, 2x – 3, 3x + y, 2xy + 5, xyz + x + y + z
• Some examples of equations are:
5x = 25,
2x – 3 = 9

4. Linear Equations
• A linear equation is like a math sentence that says two things are equal and the
highest power of the variable is just 1. It looks like this:
3x+6=21
• Here, x is the variable.
• The cool thing is, if you know the value of x, you can find out what makes the
equation true! It's like solving a puzzle to figure out the missing piece.

5. Solving Linear Equations
• 2x – 3 = 7. For x = 5,
• LHS = 2 × 5 – 3 = 7 = RHS
• x = 5 is the solution of the equation
• On the other hand x = 10 is not a solution of the
• equation. For x = 10, LHS = 2 × 10 –3 = 17.
• This is not equal to the RHS

6. Solving Equations having the Variable on
both Sides
• We now discuss how to solve such equations which have expressions with the
variable on both sides.
Solve 2x – 3 = x + 2
• General Thumb Rule
• Isolate x: First, let's get all the x's on one side of the equation.
• Get rid of the extra numbers : Now, let's kick out anything that's not x's business.
Add/ Subtract/ Divide/Multiply to simplify the equation.

7. Sample Problems

8. Reducing Equations to Simpler Form

9. Thank You