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Which statement about adding the same number to both sides of an equation is true?

Class 7Simple EquationsSimple Equations
  • AIt changes the solution by that number
  • BIt is allowed only when the number added is positive
  • CIt is allowed only after the variable is alone on one side
  • DIt leaves the solution unchanged

Step-by-Step Solution

That is the balance principle: the same operation on both sides keeps the statement true, so the solution is untouched. For example has the solution 8; adding 3 to both sides gives — the same solution, just easier to read. The number may be negative, and this rule is exactly what you use BEFORE the variable has been isolated.
Answer: D) It leaves the solution unchanged

Key idea: Translating word problems into equations

Three steps:
1. **Pick a variable** for the unknown ('let be the number of …').
2. **Translate the words into an equation** using the operations the problem describes.
3. **Solve and answer in the original units.**

Example: 'Three times a number plus 7 equals 22. Find the number.'
Let = the number. Equation: . Solve: .
Answer: the number is 5.

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