Point B is on line segment AC. Given AB
— '2m + 10, BC x, and AC
5m, determine the numerical length of AC.

We are given that:

- \( AB = 2m + 10 \)
- \( BC = x \)
- \( AC = 5m \)

Since \( B \) is a point on line segment \( AC \), the total length \( AC \) is the sum of the lengths of \( AB \) and \( BC \):

\[
AC = AB + BC
\]

Substituting the given values:

\[
5m = (2m + 10) + x
\]

Now, solve for \( x \):

\[
5m = 2m + 10 + x
\]

Subtract \( 2m \) from both sides:

\[
3m = 10 + x
\]

Now, subtract 10 from both sides:

\[
x = 3m - 10
\]

Thus, the value of \( BC \) (which is \( x \)) is \( 3m - 10 \), and the total length of \( AC \) is \( 5m \), as given.

Would you like further details or have any questions?

Here are 5 related questions:
1. What happens if the value of \( m \) is given? How does that affect \( BC \)?
2. How do you check the consistency of the segment length using different values for \( m \)?
3. What are some common mistakes when setting up such equations?
4. If \( AB \) and \( BC \) were in terms of other variables, how would the approach change?
5. How does this method extend to other geometric figures?

**Tip:** Always double-check your equation setup by reviewing how the segments add up to the total length.

Point B is on line segment AC. Given AB = 2m + 10, BC = x, and AC = 5m, determine the numerical length of AC.

Learn how to solve for the length of BC on line segment AC where AB = 2m + 10 and AC = 5m. This problem involves key algebraic and geometric concepts such as segment addition and solving linear equations. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation