Meaning Preservation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Which operation preserves the solution set of an equation: (a) multiply both sides by 3, (b) multiply both sides by 0, (c) add 7 to both sides?

Solution

  1. 1
    (a) Multiply by 3 (non-zero): preserves the equation. Valid.
  2. 2
    (b) Multiply by 0: both sides become 0, losing all information about the variable. Does NOT preserve the solution set.
  3. 3
    (c) Add 7 to both sides: preserves equality. Valid.

Answer

(a)  Preserves,(b)  Does NOT preserve,(c)  Preserves(a)\;\text{Preserves},\quad (b)\;\text{Does NOT preserve},\quad (c)\;\text{Preserves}
Multiplying by zero collapses every equation to 0=00=0, which is true for all values of xx — it destroys information about the solution set. Multiplying by a non-zero constant and adding constants are always safe.

About Meaning Preservation

Meaning preservation is the principle that valid mathematical transformations must maintain the truth and relationships of the original expression — changing form without changing content.

Learn more about Meaning Preservation →

More Meaning Preservation Examples

Example 1 easy

When solving [formula], list each algebraic step and explain why it preserves the meaning (solution

Example 2 medium

Squaring both sides of [formula] can introduce extraneous solutions. Solve the equation and check wh

Example 4 medium

A student divides both sides of [formula] by [formula], getting [formula], so [formula]. Identify th

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