the solution of the equations ax+b=0is X=a/b
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x={-b/a}
PREMISES
y=ax+b=0
CALCULATIONS
y=ax+b=0
ax+b=0
ax+(b-b)=0-b
ax+0=-b
ax=-b
ax/a=-b/a
x=
-b/a
PROOF
If x=-b/a, then the equations
ax+b=0
a(-b/a)+b=0 (Cancel the common factor a in the denominator and adjust the numerator)
-b+b=0 and
0=0 prove the root (zero) x=-b/a of the statement ax+b=0
C.H.
PREMISES
y=ax+b=0
CALCULATIONS
y=ax+b=0
ax+b=0
ax+(b-b)=0-b
ax+0=-b
ax=-b
ax/a=-b/a
x=
-b/a
PROOF
If x=-b/a, then the equations
ax+b=0
a(-b/a)+b=0 (Cancel the common factor a in the denominator and adjust the numerator)
-b+b=0 and
0=0 prove the root (zero) x=-b/a of the statement ax+b=0
C.H.
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