Point S is on line segment start overline, R, T, end overline*RT*. Given S, T, equals, 2, x, comma*ST*=2*x*, R, T, equals, 4, x, comma*RT*=4*x*, and R, S, equals, 4, x, minus, 4, comma*RS*=4*x*−4, determine the numerical length of start overline, R, S, end overline, .*RS*.

Given the problem, we have a line segment \( RT \) with a point \( S \) on it. The lengths of the segments are provided as:

- \( ST = 2x \)
- \( RT = 4x \)
- \( RS = 4x - 4 \)

Since \( S \) is on the line segment \( RT \), the total length \( RT \) should be the sum of the lengths of \( RS \) and \( ST \). Therefore, we can write the equation:

\[
RS + ST = RT
\]

Substituting the given expressions:

\[
(4x - 4) + 2x = 4x
\]

Now, let's solve this equation step by step:

1. Combine like terms on the left side:

\[
4x - 4 + 2x = 4x
\]

\[
6x - 4 = 4x
\]

2. Move all terms involving \( x \) to one side by subtracting \( 4x \) from both sides:

\[
6x - 4x - 4 = 0
\]

\[
2x - 4 = 0
\]

3. Add 4 to both sides to isolate the term with \( x \):

\[
2x = 4
\]

4. Divide both sides by 2:

\[
x = 2
\]

Now that we have \( x = 2 \), we can find the numerical length of \( RS \) by substituting \( x \) back into the expression for \( RS \):

\[
RS = 4x - 4 = 4(2) - 4 = 8 - 4 = 4
\]

Thus, the numerical length of \( RS \) is \( \boxed{4} \).

Would you like further details or have any questions?

Here are 5 related questions:

1. What would the length of \( ST \) be if \( x = 2 \)?
2. Can you verify the length of \( RT \) using the calculated value of \( x \)?
3. How would the solution change if \( RS = 4x + 4 \) instead?
4. What is the significance of the relationship \( RS + ST = RT \) in solving for \( x \)?
5. How would the problem differ if \( S \) were not between \( R \) and \( T \)?

**Tip:** After solving for \( x \), always check by plugging the value back into the original expressions to ensure the solution is correct.

Explore how to determine the numerical length of RS on line segment RT with a detailed mathematical solution. Given ST = 2x, RT = 4x, and RS = 4x - 4, learn how to calculate the length of RS using algebraic equations. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation