   SEARCH HOME Math Central Quandaries & Queries  Question from Kathy, a parent: How would you solve .07 = (1 + x)/(1+.12) - 1 Thanks! Hi Kathy.

You can do anything to one side of an equation as long as you also do it to the other side (except divide by zero, that's disallowed).

I'll show you how I'd solve this kind of problem and leave you to use this technique for your own problem.

Solve for x:

3 [ (x + 1.2) / .75 - 1] = 2

To isolate x, let's work from the outside inwards. On the left-hand-side (LHS), we have 3 times some expression in brackets. We can get rid of the three if we divide the whole LHS by 3. Then we have to do the same to the RHS. So we have:

(x + 1.2) / .75 - 1 = 2 / 3

I've removed the outer brackets now because the 3's outside canceled, so they have no further purpose. Now the LHS is some algebraic expression minus 1. To remove the minus 1, we can add 1 to both
sides, then it cancels out:

(x + 1.2) / .75 = (2 / 3) + 1

Now the LHS has something in parentheses divided by .75. If I multiply both sides by .75, I can get rid of that from the LHS:

x + 1.2 = [ (2/3) + 1 ] (.75)

And finally, I can subtract 1.2 from both sides:

x = [ (2/3) + 1 ] (.75) - 1.2

Simplifying this, x = [5/3](.75) - 1.2 = 1.25 - 1.2 = .05.

Now you try this technique with your own question.
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.