Question

3,

Answer 1

Problem 1

Answer:  x = 8

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Explanation:

The tickmarks say that TU and UV are the same length. Both are 23 units each. They combine to TU+UV = 23+23 = 46, which is the length of TV

TV = 5x+6

TV = 46

5x+6 = 46

5x = 46-6

5x = 40

x = 40/5

x = 8

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Problem 2

Answer:  QR = 53

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Explanation:

We use the same idea as the previous problem.

PQ = 6x-1 is the same length as QR

PQ+QR = (6x-1)+(6x-1) = 12x-2 = PR

Since PR = 15x-29, we can then say,

PR = 12x-2

15x-29 = 12x-2

15x-12x = -2+29

3x = 27

x = 27/3

x = 9

From there,

• PQ = 6x-1 = 6(9)-1 = 53
• QR = 53  since PQ and QR are the same length
• PQ+QR = 53+53 = 106
• PR = 15x-29 = 15(9)-29 = 135-29 = 106

This shows that PQ+QR = PR is true and it helps confirm the answer.