Please observe the solution for the following two problems :
(a) 2x + 18 = x + 25
(b) 3x + 5 = 7x - 15
(a)
2x + 18 = x + 25
2x - x = 25 - 18. -------- (1)
x = 7
(b)
3x + 5 = 7x - 15
7x - 3x = 15 + 5 ---------- (2)
4x = 20
x = 5
Explain the rules involved in transposing -
In (1)
Can 2x - x = 25 - 18
be expressed as
x - 2x = 18 - 25
In (2)
Can 7x - 3x = 15 + 5
be expressed as
3x - 7x = 15 - 5
If yes - why ?
If no - why not ?
Hope I have framed my question properly. I'm confused with transposing.
1. yes ... it is the result of multiplying the equation by -1
2. no ... the left side can come from multiplication by -1
BUT ... changing a single sign in the right side polynomial is not a legitimate operation
Can 7x - 3x = 15 + 5
be expressed as
3x - 7x = 15 - 5
NO !!!!!!!!!!!!!!!!!!!!
7x - 3x = 15 + 5
multiply both sides of the equation by -1
-1(7x-3x) = -1(15+5)
3x - 7x = -15 - 5 *****note -15 not +15
In (1)
Can 2x - x = 25 - 18
be expressed as
x - 2x = 18 - 25
===========================
multiply both sides by -1 again
-2x +x = -25 + 18
sure, fine
Thanks a lot all of you.
Transposing, also known as rearranging or isolating, is a fundamental step in solving algebraic equations. It involves moving terms from one side of the equation to the other side in order to isolate the variable.
In equation (1), we have 2x + 18 = x + 25. To isolate the variable x, we need to move the term with x (2x) to one side and the constant term (18) to the other side. We can do this by subtracting x from both sides of the equation:
2x - x = 25 - 18
Simplifying this expression gives us:
x = 7
Now let's address your question about transposing. In (1), you asked if 2x - x = 25 - 18 can be expressed as x - 2x = 18 - 25, and in (2) you asked if 7x - 3x = 15 + 5 can be expressed as 3x - 7x = 15 - 5.
The answer is no, we cannot express them in that way. When transposing terms, we can only move the variables and constants to the opposite side of the equation, but we must preserve their order. Therefore, in (1), we cannot change the order, so x - 2x = 18 - 25 is incorrect.
Similarly, in (2), the original equation is 3x + 5 = 7x - 15. We can transpose 7x to the left side and 5 to the right side by subtracting 7x and adding 5:
3x - 7x = 15 - 5
The result should be -4x = 10, not 3x - 7x = 15 - 5.
When transposing terms, it is important to keep the same order and apply operations correctly to maintain the equality of the equation.