Question

Point S is on line segment RT. Given RS = 4x – 10, ST = 2x – 10, and

Answer 1

Answer:

The numerical length of RS is 22 units

Step-by-step explanation:

∵ Point S is on the line segment RT

→ That means S divide RT into two parts RS and ST

∴ RS + ST = RT

∵ RS = 4x - 10

∵ ST = 2x - 10

∵ RT = 4x - 4

→ Substitute them in the statement above

∴ 4x - 10 + 2x - 10 = 4x - 4

→ Add the like terms in the left side

∴ (4x + 2x) + (-10 + -10) = 4x - 4

∴ 6x + (-20) = 4x - 4

∴ 6x - 20 = 4x - 4

→ Add 20 to both sides

∴ 6x -20 + 20 = 4x - 4 + 20

∴ 6x = 4x + 16

→ Subtract 4x from both sides

∴ 6x - 4x = 4x - 4x + 16

∴ 2x = 16

→ Divide both sides by 2 to find x

∴ $\frac{2x}{2}=\frac{16}{2}$

∴ x = 8

→ Substitute the value of x in Rs to find its length

∵ RS = 4(8) - 10

∴ RS = 32 - 10

∴ RS = 22 units

The numerical length of RS is 22 units