https://file.aiquickdraw.com/mathbot/file/1726581761008f7c1txsu.jpg

In the image, we are given a line segment \(AC\), which is divided into two smaller segments \(AB\) and \(BC\). The length of segment \(AB\) is represented as \(2x - 6\), and the length of segment \(BC\) is given as 18. Additionally, the total length of segment \(AC\) is given by the expression \(x + 45\).

To find the value of \(x\), we can set up the following equation based on the fact that the sum of the lengths of segments \(AB\) and \(BC\) should equal the total length \(AC\):

\[
AB + BC = AC
\]

Substitute the given expressions:

\[
(2x - 6) + 18 = x + 45
\]

Now, let's solve for \(x\):

1. Simplify the left-hand side:

\[
2x - 6 + 18 = x + 45
\]

\[
2x + 12 = x + 45
\]

2. Subtract \(x\) from both sides:

\[
2x - x + 12 = 45
\]

\[
x + 12 = 45
\]

3. Subtract 12 from both sides:

\[
x = 45 - 12
\]

\[
x = 33
\]

So, the value of \(x\) is \(33\).

Would you like more details on this solution or further clarification?

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Here are 5 related questions to deepen your understanding:

1. How would the equation change if the length of \(BC\) was a different value?
2. Can you create a similar problem where the total length of the segment is given, and you need to solve for \(x\)?
3. How would you check your solution for correctness after solving for \(x\)?
4. What other algebraic methods could you use to solve this equation?
5. How does understanding this problem help in solving geometric problems involving line segments?

**Tip**: When solving algebraic equations, always check your solution by substituting it back into the original equation to verify the accuracy.

Use the figure to write and solve an equation for x.

Learn how to solve for x in an algebraic equation involving the lengths of line segments AB and BC, where AB = 2x - 6, BC = 18, and AC = x + 45. This problem covers key algebraic concepts, including linear equations. Suitable for students in Grades 7-9.

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