Answer:
x = 3
Explanation:
You want to know how to solve 2x +3 = 9.
Solution
A solution is an equation of the form ...
x = constant
Process
You can get a clue to the solution process by considering what happens to the variable. Here, ...
- the variable is multiplied by 2
- 3 is added to the sum
The solution process reverses these operations, starting with the last one first. The properties of arithmetic and equality are used.
Undo addition
We can undo the addition of 3 by adding -3 to both sides of the equation.
2x +3 -3 = 9 -3
2x +0 = 6 . . . . . . . . . . . adding 3 and its additive inverse gives zero
2x = 6 . . . . . . . . . . . . . 0 is the additive identity element, so 2x+0 = 2x
Undo multiplication
We can undo the multiplication by multiplying by the multiplicative inverse of 2. That is, we can multiply by 1/2.
(1/2)2x = (1/2)6
1x = 3 . . . . . . . multiplying 2 and its multiplicative inverse gives 1
x = 3 . . . . . . 1 is the multiplicative identity element, so 1x = x
Please note that multiplying by 1/2 is the same thing as dividing by 2. That is, multiplication and division are inverse operations.
The solution is x = 3.
Check
It is wise to check that the solution you found makes the equation be true.
2x +3 = 9
2(3) +3 = 9 . . . . . substitute for x
6 + 3 = 9 . . . . . . . true
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Additional comment
This solution process works for just about any "solve for ..." situation, if an algebraic solution is possible. In high school math, you are introduced to just about every kind of equation we know how to solve. The list is fairly short.
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