Subtraction/Examples/x+3 = 5
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Examples of Subtraction
The equation:
- $x + 3 = 5$
has the solution:
- $x = 2$
Proof
\(\ds x + 3\) | \(=\) | \(\ds 5\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds \paren {x + 3} + \paren {-3}\) | \(=\) | \(\ds 5 + \paren {-3}\) | adding $-3$ to both sides | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds x + \paren {3 + \paren {-3} }\) | \(=\) | \(\ds 5 - 3\) | Associative Law of Addition, Definition of Subtraction | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds x + 0\) | \(=\) | \(\ds 2\) | Definition of Additive Inverse of Number, Definition of Subtraction | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds x\) | \(=\) | \(\ds 2\) | Real Addition Identity is Zero: Corollary |
$\blacksquare$
Sources
- 1967: Michael Spivak: Calculus ... (previous) ... (next): Part $\text I$: Prologue: Chapter $1$: Basic Properties of Numbers