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Ad libitum [116K]
3 years ago
12

Point R is on line segment QS. Given QS= 5x-2, QR= 3x-6, and RS=4x-2, determine the numerical length of RS.

Mathematics
1 answer:
pashok25 [27]3 years ago
8 0

Answer:

The numerical length of RS is 10 units

Step-by-step explanation:

* <em>Lets explain How to solve the problem</em>

- Point R is on line segment QS

- The length of QS is (5x - 2)

- The length of QR is (3x - 6)

- The length of RS is (4x - 2)

- <em>The length of QS is the sum of the lengths of QR and RS</em>

∵ QS = QR + RS

∴ (5x - 2) = (3x - 6) + (4x - 2)

- Simplify the right hand side by adding like terms

∴ 5x - 2 = (3x + 4x) + (-6 + -2)

∴ 5x - 2 = 7x + -8 ⇒ (+)(-) = (-)

∴ 5x - 2 = 7x - 8

- Add 8 for both sides

∴ 5x + 6 = 7x

- Subtract 5x from both sides

∴ 6 = 2x

- Divide both sides by 2

∴ x = 3

- <em>To find the length of RS substitute the value of x in its expression</em>

∵ RS = 4x - 2

∵ x = 3

∴ RS = 4(3) - 2 = 12 - 2 = 10

∴ The numerical length of RS is 10 units

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