1. ## equation

b+24=19

65=n+24

40=w+(-5)

2. Originally Posted by dianna
b+24=19

65=n+24

40=w+(-5)
Poor dianna. Nobody cares for you?

Let us see, you want to solve for the unknowns in the 3 equations, right?

Okay.

In any equation, to solve for the unknown is to find ways to isolate the unknown alone by itself, with no attached numerical coefficient or the number attached to it, in one side of the equation.

b +24 = 19.
To isolate b alone in the lefthand side, we have to transpose the 24 to the righthand side. Subtract 24 from both sides,
b = 19 -24

--------------------------------------------
65 = n +24
To leave n alone in the righthand side (RHS), we move the 24 to the lefthand side (LHS). Subtract 24 from both sides,
65 -24 = n
41 = n
Or,

-------------------------------------------
40 = w +(-5)

Two ways to do that.

One way is to add right away the -5 to w.
40 = w -5
To leave w alone in the RHS, we add 5 to both sides...

Er, to remove a number from any side, we make it zero in that side. So if the number to be removed is positive, we subtract the same number to both sides. If the number to be removed is negative, like the -5 above, we add 5 to both sides. Because -5 +5 = 0 and the initial -5 in the RHS disappears. .

To continue,...
40 +5 = w
45 = w

The other way is to transpose the (-5) to the LHS, thus,
40 = w +(-5)
To leave w alone in the RHS, we subtract (-5) from both sides,
40 -(-5) = w
40 +5 = w
45 = w
w = 45 -----------------------same. I assume you know negative times negative is positive.

---------------------------------
Later on, you will see that transposing any number to the other side of the equation is simply changing the sign of that number in the new location.

In example #1 above, we transpose the +24 by making it -24 in its new location.

In example #2, the +24 becomes -24 again when transposed to the other side.

Etc.

Sorry, I have to go.