Solution 1

Updated: 2/26/2020

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- 3. Okay let's try it does that mean we divide both sides by 3?
- 1. Remember that we want a final answer where x is on one side and there is a number on another side: x > 6
- 3x +6 > 2x -4Talk with your group about how you would solve this inequality and then try out your method.
- 4. Yes we would have to divide each term by 3, which would be kinda messy because 2 and 4 aren't divisible by 3.
- 2. I think we should divide by 3 first
- 5. I am going to try it and see what happens
- What is the pattern?What do you observe?0 -> 12 -> 24 -> 36 -> 4
- 1. So today we are going to look at inputs and outputs and create a function for the pattern. If you are stuck start making observations. Once you have a function, use the computer to see if the function is accurate for the given points.
- 5. Once you have a equation that matches the input and output see if you can find other equations that match
- 2. All of the y-values are increasing by 1
- 5. Okay so I don't know if this helpful but another observation is that the x-values are increasing by 2
- 4. Mm I don't think so. That would only work for the first x,y pair
- 3. So does that mean the function is just adding 1 to each x-value?
- 5. I also think substitution works well here, I think it probably always works well when it is easy to solve for one of the variables
- Decide what way you prefer to solve this system of equations (substitution, elimination, or graphing- no calculator). Make sure to try all the methods.4x+y=23y+6x=9
- 4. Substitution is also pretty easy - you can solve for y in the first equation.
- 1. Try the three different methods of solving and then talk with your group and advocate for which method you preferred for this problem. If you have time see if you can create some rules about when you should use each method.
- 2. So I tried elimination and it wasn't too tricky, I multiplied by the first equation by 3
- 3. Yeah I agree elimination is pretty easy. I don't think graphing is good here because you had to solve each equation for y
- 3. We could also subtract 3x at the same time as adding 4.
- 7. I think when you divide by a negative you have to switch the inequality sign, that's what I did
- 5. I got x < -10
- 2. I think we should add 4 to both sides
- 4. Okay cool let's try it.
- 6. Mm I didn't get that
- What is the pattern?What do you observe?0 -> 12 -> 24 -> 36 -> 4
- 4. Okay for my slope I got 1/2, should we try to graph this function and see if it matches?
- 2. I can't see an obvious pattern...
- 7. Mm I don't think that works because we have to multiply both sides by 2, so it would be 2y = x+ 2
- 3. Yeah me neither. Should we try finding the slope?
- 6. Okay so now we see if we can find other equations. Let's try y=x+2
- 5. Awesome I graphed the function y=1/2x +1 and it matches the points!
- 6. I think elimination is the easiest. You can just divide the 2nd equation by 3 and then y is eliminated when you subtract the 2nd equation from the 1st
- 4. Yeah graphing takes a lot of time - I don't think it makes sense for this problem. I'm not sure graphing ever makes sense?
- 5. Personally I think graphing because I'm a visual person
- 3. Yup that's what I did for substitution. I think substitution is the best method here
- 7. Why do you like elimination more than substitution?
- 2. For substitution I did y, did everyone else do that?