# Hello; need some help solving 1/1 - 3/2 + w = 60

#### Guitarman

##### New member
I'm having some diffulty with some math problems.

. . .1/1 - 3/2 + w = 60

...or if this is easier: 1 over 1 - 3over 2 + w = 60. The 3/2 + w is a fraction and 1 is over all of it.

I've done the work and believe the answer to be w = 120 but am not sure exactly. I'm not looking for the answer, just want to know if I'm way off or what. This is what I've done:

. . .2 + w/1 - 3 = 60

. . .2 + w/-2 = 60(-2)

. . .-w = -120

. . .w = 120

Thank you!

#### stapel

##### Super Moderator
Staff member
I'm sorry, but I'm not clear on what the expression on the left-hand side of the equation is. At first, it looks like:

. . . . .(1/1) - (3/2) + w

But it might also be:

. . . . .(1/1) - 3/(2 + w)

. . . . .1/[1 - 3/(2 + w)]

. . . . .1/[1 - (3/2) + w]

...or something else.

Please use grouping symbols (as above) to clarify. Thank you.

Eliz.

#### Guitarman

##### New member
1/[1 - 3/(2 + w)]=60

its that one. its basically a complex fraction. its kinda hard to type it out. sorry.

#### stapel

##### Super Moderator
Staff member
Guitarman said:
1/[1 - 3/(2 + w)] = 60
So the equation is as follows:

. . . . .$$\displaystyle \L \frac{1}{1\,-\,\frac{3}{2\,+\,w}}\,= \,60$$

Since the numerator is equivalent to "1/1", since 1 - 3/(2 + w) = [(2 + w) - 3]/(2 + w) = (w - 1)/(2 + w), and since, when dividing by a fraction, one inverts and multiplies, this simplifies as:

. . . . .$$\displaystyle \L \frac{2\,+\,w}{w\,-\,1}\, =\,60$$

"Cross-multiplying", we get:

. . . . .$$\displaystyle \L 2\,+\,w\,= \,60w\,-\,60$$

Solve by the usual methods.

Note: The solution to any "solving" exercise may be checked by plugging it back into the original problem. You have proposed "w = 120" as a solution.

Checking:

. . . . .$$\displaystyle \L \frac{1}{1\,-\,\frac{3}{2\,+\,(120)}}$$

. . . . . . .$$\displaystyle \L =\,\frac{1}{1\,-\,\frac{3}{122}}$$

. . . . . . .$$\displaystyle \L =\,\frac{1}{\left(\frac{122\,-\,3}{122}\right)}$$

. . . . . . .$$\displaystyle \L =\,\frac{1}{\left(\frac{119}{122}\right)}$$

. . . . . . .$$\displaystyle \L =\,\frac{122}{119}$$

. . . . . . .$$\displaystyle \L \neq\,60$$

So the solution is likely some other value.

Eliz.

#### Denis

##### Senior Member
1/[1 - 3/(2 + w)]=60 ; you went from that to:
2 + w/1 - 3 = 60

and followed that with:
2 + w/-2 = 60(-2)
-w = -120
w = 120

You are GUESSING; your steps are VERY wrong;
you need to have a talk with your teacher...or to listen in class...