Two-Step Equations

Date: 01/30/2003 at 19:19:34
From: Tara
Subject: Two-step equations

What are two different two-step equations that have 1.2 as their 
solution?

2x - 1 + 1 = 2 + 1 = 3

Date: 01/30/2003 at 21:07:56
From: Doctor Rick
Subject: Re: Two-step equations

Hi, Tara.

You wrote down the first step in solving the equation 2x - 1 = 2, 
right? The solution is 3/2. What you have to do is different from 
solving an equation; you need to work it the other way around, 
starting with the solution and building the equation.

A two-step equation usually has a number on one side and an expression 
with a variable and two operations on the other side. I'll make one 
that has the solution 3.5, so you can do yours on your own.

I start with the number 3.5. I will make the two operations 
multiplication and addition (I'm not sure whether your two-step 
equations can use other operations or not). I pick any number to 
multiply by 3.5; I will pick an even number so the result is an 
integer, but that's not required. I'll choose 4:

  3.5 * 4 = 14

Then I pick a number to add to this. I'll take a negative number just 
for fun: -9.

  3.5 * 4 + -9 = 5

Now I can go and replace the solution (3.5) by a variable. I'll pick 
the variable t:

  t * 4 + -9 = 5

I can clean this up a bit:

  4t - 9 = 5

That's the equation. When you solve it, you undo these steps in 
reverse. First "unsubtract" the 9 (add 9):

  4t - 9 + 9 = 5 + 9
  4t = 14

Then "unmultiply" the 4 (divide by 4):

  4t/4 = 14/4
  t = 3.5

Now it's your turn: Come up with two two-step equations whose 
solution is 1.2.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/