Linear equation using segment | Geometry | 8th grade | Khan Academy

TL;DR

Given the lengths of different line segments and an equation, find the value of x and the length of a specific segment.

Transcript

So we have this line segment JL here, and we have point K that also sits on that segment. And they tell us that JK is equal to 7x plus 9. So this distance right over here is equal to 7x plus 9. Then they tell us that JL is equal to 114. So JL is the entire length of the segment. So this entire thing is equal to 114. Then they tells us that KL is eq... Read More

Key Insights

• 🫥 The problem involves finding the length of a line segment using algebraic equations.
• 🫥 The given information includes the lengths of different line segments as well as an equation representing the total length.
• ☺️ By solving for x, the length of the desired line segment can be determined.
• 🍉 Combining like terms and applying algebraic operations are necessary steps in solving the problem.
• ❓ Understanding the given equation and identifying the corresponding segment lengths are crucial.
• ☺️ Substituting the value of x into the equation yields the final result.
• ❓ The importance of careful calculation and attention to detail is emphasized.

Questions & Answers

Q: What is the objective of the problem?

The objective is to find the length of line segment KL by solving for x using the given equation and lengths of other line segments.

Q: How is the equation set up to represent the problem?

The equation JK + KL = 114 is used, with JK represented as 7x + 9 and KL as 9x + 9.

Q: How is the equation simplified to find x?

By combining like terms, 7x + 9 + 9x + 9 is simplified to 16x + 18 = 114. Subtracting 18 from both sides and dividing by 16 yields x = 6.

Q: What is the length of line segment KL?

The length of KL is found by substituting x = 6 into 9x + 9, resulting in 9(6) + 9 = 63.

Summary & Key Takeaways

• The video explains how to find the length of line segment KL by solving for x using given information about the lengths of other line segments.

• The equation JK + KL = 114 is used to represent the total length of the segment, with JK = 7x + 9 and KL = 9x + 9.

• By combining like terms and simplifying the equation, x is found to be 6, and the length of KL is determined to be 63 units.