Math Problem Statement
Point Q is on line segment PR. Given PR = 2x, PQ = 5x - 4, and QR = x, determine the numerical length of PR
Solution
We are given that:
Since (because is on line segment ), we can write the equation:
Substituting the given values:
Now, simplify the equation:
Subtract from both sides:
Add 4 to both sides:
Divide by 4:
Now, substitute into the expression for :
Thus, the numerical length of is .
Would you like more details on any step or have any further questions? Here are some related questions to explore:
- What would change if were given as instead of ?
- How would the solution differ if were negative?
- What happens if point divides in a 3:2 ratio?
- Can you find the lengths of and after solving for ?
- How would this process change if was an unknown constant instead of ?
Tip: When solving problems involving segments, always use the sum of smaller segments to express the full segment length as an equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Segment Addition
Formulas
PQ + QR = PR
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 6-8
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