MathIsland · We are all mathematicians.
Equations
Explain why equivalent operations on both sides help find an unknown.
Start with the picture
Solving an equation uses permitted equivalent operations to find its solutions.
Check with another example
1. To isolate x in x+5=12, what should we do?
- Subtract 5 only on the left
- Add 5 to both sides
- Subtract 5 from both sides
My reason
2. What is the solution of 3x=15?
- 5
- 12
- 45
My reason
3. What is x when 2x+3=11?
- 7
- 4
- 8
My reason
Explain in your own words
Explain changing a sign across an equation in terms of operations on both sides.
Answers and reasons
1. Subtract 5 from both sides
Yes. x=12−5=7, and substituting gives 7+5=12.
2. 5
Divide both sides by 3: x=5. Check that 3×5=15.
3. 4
Subtract 3, then divide by 2. Checking gives 2×4+3=11.
Subtracting 3 from both sides of x+3=7 cancels +3 on the left and leaves −3 on the right.