Subtraction/Examples/x+3 = 5

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