Question

Consider this double number line.


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Answer 1

a) 3/4x = 21

b) mark the bottom number line in units of 1/4x; mark the top number line in units of 7

Explanation:

a) You are asked to equate the two values shown:

`(3)/(4)x=21`

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b) You may notice that 3/4x is 3 times (1/4x), and that 21 is 3 times 7. That is, 1/4x corresponds to 7. Then the bottom number line can be marked in units of 1/4x, and the top number line in units of 7. For example, the markings might be ...

(bottom line, top line) = (-5/4x, -35), (-x, -28), (-3/4x, -21), (-1/2x, -14), (-1/4x, -7), (0, 0), (1/4x, 7), (1/2x,14), (3/4x, 21) [shown], (x, 28), (5/4x, 35)

Of course, the spacing between 1/4x marks will be 1/3 of the space between 0 and 3/4x. You can extend the markings even farther in each direction.

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You see that x = 28, but that doesn't seem terribly relevant to the problem.

Answer 2

Part A)

Set the two values equal to each other:

3/4x = 21

Divide both sides by 3/4:

X = 21 / 3/4

X = (21*4)/3 = 84/3 = 28

Part B)

You have the value of X from part A, so multiply 28 by different values to get a new number which would be the number to use on the top number line:

1/2(28) = 14 So between the 0 and 28 add the number 14 on the top line and 1/2x on the bottom line.

1(28) = 28, so to the right of 21 put 28 on the top lone and 1X on the bottom line.