this means that we want to get b on one side of the equation by itself. so get rid of everything on the same side with b.

.......subtract from both sides

.........now if we can divide by it.

Let be the smallest even integer.Three times the larger of 2 consecutive even intergers, decreased by the smaller is 58. Find the numbers.

Then is the next even integer.

we are told that 3 times , subtracting the smaller is 58. thus,

now solve for so you can find the integers.

Let the first integer beFind 3 consecutive intergers such that the sum of the first two is 74 more than the third.

then the next is

and the largest is

the sum of the first two is 74 + the third. thus,

now solve for to find the integers

Let be the length of the first piece,A pipe is 48 inches long. David wants to cut the pipe into three pieces so that the second piece is 1 inch less than the length of the third. The first piece is 5 times as long as the third. How long is each piece?

Let be the length of the second piece,

Let be the length of the third piece,

then we have .................(1)

since the second piece is 1 inch less than the length of the third, we have:

.....................(2)

since the first piece is 5 times as long as the third, we have:

........................(3)

thus we obtain the system:

......................(1)

............................(2)

.............................(3)

now solve this system to get

if you do not know how to solve simultaneous equations, you can do this in one variable.

Let the length of the third be

then the length of the second is

and the length of the first is

the pieces add up to 48, so:

now just find , and then substitute its values into the equation to find the other pieces

Let's keep this in one variable:Ron runs a ski train. One day he noticed that the train contained 13 more women than men *including himself*. If there were a total of 165 people on the train, how many of them were men?

Let the number of men be .

since the train contained 13 more women than men, the number of women is .

these must add up to 165 people, thus:

now solve for