Math Problem Statement
If DF = 9x - 39, find EF. DF = DE + EF, where DE = 47 and EF = 3x + 10.
Solution
Let's solve the problem in the image.
We are given:
The relationship is:
Substituting the given values:
Now, let's solve this equation:
Simplifying the right side:
Subtract from both sides:
Add 39 to both sides:
Divide by 6:
Now that we know , let's find .
Substitute into :
So, .
Would you like any more details or have any questions?
Here are five related questions to expand on this problem:
- How would the result change if was expressed as instead of ?
- What would happen if was expressed in a quadratic form?
- Can you solve for if were given as a constant number, say 150?
- What if the equation included more segments on the line, such as an additional point between and ?
- How do equations change if distances between points are defined in terms of different variables?
Tip: Always combine like terms and simplify the equation step by step to avoid mistakes.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
DF = DE + EF
Theorems
Equation Balancing Theorem
Suitable Grade Level
Grades 8-10