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denis23 [38]
3 years ago
13

From the set {6, 16, 24}, use substitution to determine which value of x makes the inequality true. 4 + x < 20 A. 16 B. 6 C.

none of these D. 24
Mathematics
1 answer:
o-na [289]3 years ago
6 0
<h3>Answer: B. 6</h3>

================================================

Explanation:

In math, the term "substitution" basically means "replace". Keep in mind that x is a placeholder for a number. Think of it as a box we place a number inside.

We have the items {6, 16, 24} to use as replacements for x. We only do one number at a time

Let's try x = 6

4 + x < 20

4 + 6 < 20 ... replace x with 6

10 < 20 ... this is a true statement as 10 is less than 20

So x = 6 is a solution

Let's try x = 16

4+x < 20

4+16 < 20

20 < 20 ... this is false because we can't have a number smaller than itself

Lastly, let's try x = 24

4+x < 20

4+24 < 20

28 < 20 ... also false; 28 is not smaller than 20

We've shown that x = 16 and x = 24 are not solutions. Only x = 6 is a solution from the set {6,16,24}. This is why the answer is choice B.

-----------------

Alternative method:

4+x is the same as x+4. We can add two numbers in any order we want.

x+4 < 20 solves to x < 16 after subtracting 4 from both sides. So the set of solutions is anything smaller than 16. Looking at {6,16,24} we see that the only allowed answer is x = 6.

x = 16 is not a solution because x < 16 would turn into 16 < 16, but again we can't have a number smaller than itself.

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D(7, 3), E(8, 1), and  F(4, -1)

We calculate the squared distances between the points:

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The probability  that a matchbox will have one or fewer matches with a flaw is 0.9855 or 98.55%.

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