Question 797244: What is the value of x in the equation 2x – 3 = 9 – 4x?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Given:
(1) 2x - 3 = 9 - 4x
The idea is to get all the terms that include the factor x on one side of the equals sign and all of the constant terms (terms that do not contain the variable x) on the other side of the equals sign. This is done by first adding or subtracting terms from one side or the other. Remember that we MUST do the same operation to BOTH sides of the equation in order to keep the equality.
First add 3 to each side of (1) to get
(2) 2x - 3 + 3 = 9 + 3 - 4x
The reason we added 3 was eliminate the -3 on the left side, leaving only an "x term".
Now combine like term to get
(3) 2x + 0 = 12 - 4x or
(4) 2x = 12 - 4x
Now add 4x to each side to get
(5) 2x + 4x = 12 - 4x + 4x
Again the reason we add 4x is to eliminate the -4x.
Now combine like term to get
(6) 6x = 12 + 0 or
(7) 6x = 12
Now you want to solve for x all by itself, not 6x. So your next step is to DIVIDE both sides by 6 to get
(8) 6x/6 = 12/6 or
(9) x = 2
Now you must check your answer. You do this by putting 2 for x in the ORIGINAL given equation, (1) in this case.
Is (2*2 - 3 = 9 - 4*2)?
Is (4 - 3 = 9 - 8)?
Is (1 = 1)? Yes
Answer: The value of x that satisfies the equation 2x - 3 = 9 - 4x is 2. This is called the solution to the equation, i.e. find the value of the variable(s) that makes the equality true.
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