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Solving Linear Equations
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Solving Linear Equations
📚 Part 1: Understanding Inverse Operations
1. Match each operation with its inverse operation:
1. Addition (+)
2. Multiplication (×)
3. Taking the 5th power
4. Subtraction (-)
A. Taking the 5th root
B. Division (÷)
C. Addition (+)
D. Subtraction (-)
2. Circle the correct first step to solve: 3x + 7 = 22
Divide both sides by 3
Subtract 7 from both sides
Add 7 to both sides
Multiply both sides by 3
🔢 Part 2: Solving Simple Linear Equations
3. Solve: x - 7 = 18
4. Solve: 3x + 5 = 20
5. Solve: 2y - 9 = 15
6. Check all the steps needed to solve 4x - 12 = 8:
Add 12 to both sides
Subtract 4 from both sides
Divide both sides by 4
Multiply both sides by 4
⚡ Part 3: Equations with Powers
7. Solve: x⁵ - 7 = 18
Show all steps clearly
8. Solve: y³ + 4 = 12
9. Fill in the missing steps to solve x⁴ - 15 = 1:
Step 1: x⁴ - 15 = 1
Step 2: x⁴ = _________ (add _____ to both sides)
Step 3: x = _________ (take the _____ root of both sides)
10. Circle the correct solution to z² - 9 = 16:
z = 5
z = ±5
z = 7
z = 25
✓ Part 4: Checking Solutions
11. Check if x = 3 is the correct solution to 2x + 4 = 10 by substituting back into the original equation:
12. Solve and then check your answer: 5x - 8 = 17
Solution:
Check:
13. True or False: When checking a solution, both sides of the equation should give the same value.
True
False
🌟 Part 5: Challenge Problems
14. Solve: 3(x - 4) = 15
15. A scientist measures that the volume of a cube is 32 cubic centimetres. If the volume formula is V = s³ (where s is the side length), find the side length of the cube.
Equation to solve: s³ = 32
The side length is _______ centimetres.
16. Explain in your own words why we use inverse operations to solve equations:
17. What is one strategy you can use if you get stuck while solving an equation?
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