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/
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