Plugging In: Using Good Numbers

The larger of two negative consecutive even integers $$2t$$ and $$2(t-1)$$ is multiplied by 3 and then added to the smaller of the two original integers. Which of the following represents the result of this operation?

Incorrect. __Plug In__ a good number such as $$t=-3$$. The negative numbers in the problem become $$2(-3)=-6$$ and $$2(-3-1)=-8$$. The larger of the two is -6. Just work the problem with the number you chose until you get a numerical answer $$(-6)×3+(-8)=-26$$. That's your target. Be sure to check all five answer choices before you take your pick. This answer choice is nothing near your target. __POE__ and move on.

Incorrect. __Plug In__ a few good numbers to see that for each number you choose, you get a different *goal* (without changing, of course, the answer choice that is always correct). __POE__ and move on.

Incorrect. The correct answer must depend on the value of $$t$$ and cannot be a single number such as 3. To see that this is the case, __Plug In__ a few good numbers. For each number you choose, you will get a different *goal*. __POE__ and move on.

Did you __Plug In__ $$t=-2$$?

Be sure to __check all five answer choices__ before you pick the one choice that matches your target. Try to not use numbers that appear in the question or in the answer choices since these cause multiple choices matching your *goal*.

How did you solve this problem?

While algebra may have worked this time, it may not work the next time. The level of difficulty of that problem is no higher than medium. If you solved it algebraically, you should be able to solve it using __Plugging In__ in the same amount of time. If this is not the case, it is because you are not proficient enough with __Plugging In__. Be sure to __Plug In__ more often so that you'll be able to use it in harder questions as well.

That's great. Identifying a __Plugging In__ problem is the first step. Solving is the second. Be sure to use __Plugging In__ as often as you can so that you will gain the experience needed to solve harder questions effectively.

Incorrect. __Plug In__ a good number such as $$t=-3$$. The negative numbers in the problem become $$2(-3)=-6$$ and $$2(-3-1)=-8$$. The larger of the two is -6. Just work the problem with the number you chose until you get a numerical answer $$(-6)\times 3+(-8)=-26$$. That's your target. Be sure to check all five answer choices before you take your pick. This answer choice is nothing near your target. __POE__ and move on.

Correct. __Plug In__ a good number such as $$t=-3$$. The negative numbers in the problem become $$2(-3)=-6$$ and $$2(-3-1)=-8$$. The larger of the two is -6. Just work the problem with the number you chose until you get a numerical answer $$(-6)\times 3+(-8)=-26$$. That's your *goal*. Be sure to check all five answer choices before you take your pick. All the other answer choices are eliminated for this Plug-In, so this is the right answer choice.

$$-2$$

$$3$$

$$6t-2$$

$$8t-2$$

$$-2-4t^2$$

Yes, I did.

No, I didn't.

I used algebra.

I used __Plugging In__.

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