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
