equations

[jdessler]

if you have an problem like the on below and it says to subtract -23 from each sided to get the answer. so far so good

Because an equation represents a scale, it can also be manipulated like one. The diagram below shows a simple equation and the steps to solving it.

Initial Equation / Problem x + 23 = 45

Subtract 23 from each side x + 23 - 23 = 45 - 23

Result / Answer x = 2

(But then you get a problem like the one below)

The diagram below shows a more complex equation. This equation has both a constant and a variable on each side. Again, to solve this you must keep both sides of the equation equal; perform the same operation on each side to get the variable "x" alone. The steps to solving the equation are shown below.


Initial Equation / Problem: x + 23 = 2x + 45

Subtract x from each side x - x + 23 = 2x - x + 45
Result 23 = x + 45

Subtract 45 from each side 23 - 45 = x + 45 - 45
Result -22 = x

Answer x = -22

my question is how do you know what number or letter that has to be subtracked, that is where I am confused.

can somebody help

[nona.m.nona]

Initial Equation / Problem: x + 23 = 2x + 45

Subtract x from each side x - x + 23 = 2x - x + 45
Result 23 = x + 45

Subtract 45 from each side 23 - 45 = x + 45 - 45
Result -22 = x

Answer x = -22

my question is how do you know what number or letter that has to be subtracked, that is where I am confused.

There is no rule; the choice of which term to move is your own. With experience, however, one learns that it is usually simpler to move whichever is the smaller term, as this assists in reducing the number of negatives in one's steps.

To convince yourself that this is indeed the case, you may wish to solve the above exercise in a different way, such as by subtracting the 23 and the 2x. After you divide through by -1, what is your final result?