# (23)/(120x) = 1/5. Solve for X

1. Nov 25, 2013

### 939

How is it done?

2. Nov 25, 2013

### Staff: Mentor

Just multiply both sides by 120*x and remember that this works as long as 120*x =/= 0 which means
that x=/=0 in your final solution because dividing by zero is not defined.

3. Nov 25, 2013

### Mentallic

Remember that

$$a\cdot\frac{b}{c} = \frac{a}{c}\cdot b =\frac{ab}{c}$$

(The dot means multiply) so if we multiply

$$\frac{23}{120x}=\frac{1}{5}$$

by the denominator in the left fraction (which is 120x) then we get

$$120x\cdot\frac{23}{120x}=120x\cdot\frac{1}{5}$$

And now we can cancel 120x from the left side because

$$120x\cdot\frac{23}{120x} = \frac{120x}{120x}\cdot 23 = 1\cdot 23=23$$

So we now have

$$23=\frac{120x}{5}$$

Now you can solve the rest in the usual way you've been solving equations.
Also, keep in mind that you can have just multiplied through by x rather than 120x.

4. Nov 25, 2013

### Student100

This problem looks like it was made for cross multiplication, is that what they're teaching you right now?

5. Nov 25, 2013

### Staff: Mentor

As an alternative, if two fractions are equal, then their reciprocals are equal.

IOW, if a/b = c/d, then b/a = d/c, barring of course the possibility that any of the numbers are zero.

In the context of this problem, you can rewrite 23/(120x) = 1/5 as 120x/23 = 5.