SOLUTION: How are addition and multiplication used to sovle a linear equation? Demonstrate by solving 15x + 7 = 31 + 3x
I can sovle it 15x + 7 - 7 = 31 - 7 +3x
15x = 24 +3x
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: How are addition and multiplication used to sovle a linear equation? Demonstrate by solving 15x + 7 = 31 + 3x
I can sovle it 15x + 7 - 7 = 31 - 7 +3x
15x = 24 +3x
15x - 3x = 31 + 3x - 3x
12x = 24
x = 2
I dont know how to explain how are addition and multiplication used to solve a linear equation.
This question is from textbook
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The idea is that you never subtract, rather you add the additive inverse, and you never divide, you multiply by the reciprocal (also called the multiplicative inverse).
Add -7 to both sides:
 = 31 + (-7) + 3x)
Add 
to both sides:
 = 24 + 3x + (-3x))
Multiply both sides by the reciprocal of the coefficient on 
, namely 
\cdot 12x = \left(\frac{1}{12}\right)\cdot 24)
The point being that Addition and Multiplication are the two basic operations, while subtraction and division are simply inverse operations defined for convenience. Both addition and multiplication are commutative over the real numbers, that is:
and
But subtraction and division are not commutative, that is:
and
John
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