Tip #41 to Get a Top ACT Math Score

Answers

Easy

1. If |4 – m| = 12, then m =?
   1. 8 or 0
   2. 16 or –8
   3. –16 or –8
   4. 16 or 8
   5. 0 or –8

Medium

2. The temperature t in a certain country in spring is modeled by the inequality |t – 12| ≤ 20. Which of the following is not in that range?
   6. 32
   7. 16
   8. –4
   10. –6
   11. –16
3. If |1 + 2x| < 10, which of the following is a possible value of x?
   1. –6
   2. –5
   3. 5
   4. 6
   5. 10
4. If |x| = x + 8, then x =?
   6. –6
   7. –4
   8. –2
   10. 6
   11. 10

Hard

5. Which of the following expressions, if any, are equal for all real numbers m?
   1. 
   2. |–m|
   3. –|m|
   1. I and II only
   2. I and III only
   3. II and III only
   4. I, II, and III
   5. None of the expressions are equivalent.

Answers

1. B "Use the Answers." Try each answer choice in the equation. Choice B is correct, since |4 – 16| = |–12| = 12 and |4 – (–8)| = |12| = 12.
2. K Again, "Use the Answers." Try each answer choice in the question. The one that does not work is our answer. Choice K is correct since |–16 – 12| = |–28| = 28 which is not ≤ 20.
3. B Yet again, "Use the Answers." Try each answer choice in the question. Choice B is correct, since |1 + 2(–5)| = |1 – 10| = |–9| = 9 which is less than 10. All other choices do not work.
4. G And yet again, "Use the Answers." Try each answer choice in the question. Choice G is correct, since |–4| = 4 =–4 + 8. All other choices do not work.
5. A "Make It Real." This question is way too theoretical, so just choose real numbers for the variable. Then it's easy! Let's try a positive and then a negative number. First, let's say m = 5. So
   1. 
   2. |–5| = 5
   3. –|5| =–5

When m = 5, choices I and II are equal. Next, let's try m = –4.

1. 
2. |–(–4)| = 4
3. –|(–4)| =–4

So when m = – 4, choices I and II are still equal, and choice A is correct.

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