Question Point S is on line segment \( \overline{R T} \). Given \( S T=2 x, R T=4 x \), and \( R S=4 x-4 \), determine the numerical length of \( \overline{R S} \). Answer Attempt 1 out of 3 \( R S=\square \) Show Examples Video

To determine the numerical length of \( \overline{RS} \), let's analyze the given information step by step. **Given:** - \( ST = 2x \) - \( RT = 4x \) - \( RS = 4x - 4 \) - Point \( S \) is on line segment \( \overline{RT} \), which means: \[ RS + ST = RT \] **Setting Up the Equation:** \[ RS + ST = RT \] Substitute the given expressions: \[ (4x - 4) + 2x = 4x \] **Simplifying the Equation:** \[ 4x - 4 + 2x = 4x \] \[ 6x - 4 = 4x \] **Solving for \( x \):** \[ 6x - 4 = 4x \] Subtract \( 4x \) from both sides: \[ 2x - 4 = 0 \] Add 4 to both sides: \[ 2x = 4 \] Divide both sides by 2: \[ x = 2 \] **Finding \( RS \):** Now that we have the value of \( x \), substitute it back into the expression for \( RS \): \[ RS = 4x - 4 \] \[ RS = 4(2) - 4 \] \[ RS = 8 - 4 \] \[ RS = 4 \] **Answer:** The numerical length of \( \overline{RS} \) is **4 units**.