Ethiopian Grade 9 Mathematics - Unit 3 Presentation
1. Objectives
By the end of this lesson, you will be able to:
Define a linear equation in one variable.
Solve linear equations using addition, subtraction, multiplication, and division properties.
Identify the variable, coefficients, and constants in an equation.
Verify your answers through substitution.
2. Notes
What is a Linear Equation?
A linear equation in one variable is an equation that can be written in the form: ax + b = c, where a, b, c are real numbers and a ≠ 0.
Steps to Solving:
Simplify: Clear parentheses using the distributive property and combine like terms.
Isolate the Variable: Move all terms with the variable to one side and constants to the other.
Apply Inverse Operations: Use subtraction to undo addition, and division to undo multiplication.
Check: Substitute your answer back into the original equation.
3. Examples
Example 1: Basic Solving
Solve: 3x - 12 = 18
1. Add 12 to both sides: 3x = 30
2. Divide by 3: x = 10 Verification: 3(10) - 12 = 30 - 12 = 18. Correct!
Example 2: Variables on Both Sides
Solve: 5x + 4 = 2x + 16
1. Subtract 2x from both sides: 3x + 4 = 16
2. Subtract 4 from both sides: 3x = 12
3. Divide by 3: x = 4
4. Practice Questions (20 Items)
Click the buttons to see the solution for each problem.
Q1: Solve x + 9 = 20
Subtract 9 from both sides: x = 20 - 9. Final Answer: x = 11
Q2: Solve 2x - 5 = 11
Add 5 to both sides: 2x = 16. Divide by 2: x = 8. Final Answer: x = 8
Q3: Solve 3(x + 2) = 15
Distribute 3: 3x + 6 = 15. Subtract 6: 3x = 9. Divide by 3: x = 3. Final Answer: x = 3
Q4: Solve x/4 = 7
Multiply both sides by 4: x = 7 * 4. Final Answer: x = 28
Q5: Solve 10 - x = 4
Subtract 10: -x = -6. Multiply by -1: x = 6. Final Answer: x = 6
Q6: Solve 4x + 10 = 2x + 20
Subtract 2x: 2x + 10 = 20. Subtract 10: 2x = 10. Divide by 2: x = 5. Final Answer: x = 5
Q7: Solve 5(2 - x) = 15
Distribute 5: 10 - 5x = 15. Subtract 10: -5x = 5. Divide by -5: x = -1. Final Answer: x = -1
Q8: Solve x/2 + 3 = 10
Subtract 3: x/2 = 7. Multiply by 2: x = 14. Final Answer: x = 14
Q9: Solve 3x + 1 = x + 7
Subtract x: 2x + 1 = 7. Subtract 1: 2x = 6. Divide by 2: x = 3. Final Answer: x = 3
Q10: Solve 2(x - 4) = 3(x + 1)
Expand: 2x - 8 = 3x + 3. Subtract 2x: -8 = x + 3. Subtract 3: x = -11. Final Answer: x = -11
Q11: Solve x/3 + x/2 = 10
Find LCD (6): 2x/6 + 3x/6 = 10 -> 5x/6 = 10. Multiply by 6: 5x = 60. Divide by 5: x = 12. Final Answer: x = 12
Q12: Solve 0.5x = 4
Divide by 0.5 (same as multiplying by 2): x = 4 / 0.5 = 8. Final Answer: x = 8
Q13: Solve 7x - 4 = 5x + 8
Subtract 5x: 2x - 4 = 8. Add 4: 2x = 12. Divide by 2: x = 6. Final Answer: x = 6
Q14: Solve (x + 5)/2 = 10
Multiply by 2: x + 5 = 20. Subtract 5: x = 15. Final Answer: x = 15
Q15: Solve 12x = 0
Divide by 12: x = 0/12 = 0. Final Answer: x = 0
Q16: Solve x - 1/2 = 3/2
Add 1/2 to both sides: x = 3/2 + 1/2 = 4/2 = 2. Final Answer: x = 2
Q17: Solve 3(2x - 1) = 9
Divide by 3 first: 2x - 1 = 3. Add 1: 2x = 4. Divide by 2: x = 2. Final Answer: x = 2
Q18: Solve x + x + x = 15
Combine like terms: 3x = 15. Divide by 3: x = 5. Final Answer: x = 5
Q19: Solve 20 - 2x = x + 2
Add 2x: 20 = 3x + 2. Subtract 2: 18 = 3x. Divide by 3: x = 6. Final Answer: x = 6
Q20: Solve x/5 - 1 = 1
Add 1: x/5 = 2. Multiply by 5: x = 10. Final Answer: x = 10