Simple Linear Equations

A linear equation is an equation that represents a straight line when graphed. In simple linear equations, the highest power of the variable is 1. These equations are used to find the value of an unknown variable.

1. What is a Linear Equation?

• An equation that can be written in the form ax + b = c, where a, b, and c are numbers and x is the variable.
• Examples: 2x + 3 = 7, x - 5 = 10, 4x = 20

2. Solving Simple Linear Equations

1. Isolate the variable on one side of the equation.
2. Perform the same operation on both sides to keep the equation balanced.
3. Solve for the variable.

Example 1:

Solve: x + 5 = 12
Step 1: Subtract 5 from both sides: x + 5 - 5 = 12 - 5
Step 2: x = 7

Example 2:

Solve: 3x = 15
Step 1: Divide both sides by 3: 3x/3 = 15/3
Step 2: x = 5

3. Word Problems

• Problem: Riya thinks of a number. She adds 8 to it and gets 20. What is the number?
  Solution: Let the number be x.
  Equation: x + 8 = 20
  Subtract 8 from both sides: x = 12
• Problem: 5 times a number is 35. Find the number.
  Solution: Let the number be x.
  Equation: 5x = 35
  Divide both sides by 5: x = 7

4. Practice Questions

1. Solve: x - 4 = 10
2. Solve: 2x + 3 = 11
3. Solve: y/5 = 6
4. If 7 is added to a number, the result is 15. Find the number.
5. Twice a number is 18. What is the number?

5. Key Points

• Keep the equation balanced by performing the same operation on both sides.
• Check your answer by substituting it back into the original equation.
• Linear equations have only one solution.

6. Summary

• Simple linear equations help us find unknown values.
• They are solved by isolating the variable using addition, subtraction, multiplication, or division.
• Practice helps in mastering the steps to solve equations.