Problem 1
Answer: x = 8
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Step-by-step 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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Step-by-step 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.