Math Problem Statement
suppose for some value of x the solution to the equation 2.5 (y-x)=0 is y=6. what must be true about x? justify your conclusion
Solution
We are given the equation:
And we're told that when the solution is , we need to find what must be true about .
Step 1: Analyze the equation
The given equation is:
Since we know , substitute into the equation:
Step 2: Solve for
Now simplify the equation:
Solving for , we find:
Conclusion:
For the equation to hold true with , the value of must also be .
Justification:
The equation implies that must be zero because multiplying by 2.5 doesn't affect the equality. Thus, for , we must have , which leads to .
Would you like more details on the steps or any clarification? Here are some related questions:
- What happens to the equation if ?
- How does multiplying an equation by a constant affect its solution?
- What other equations would have the same solution for ?
- How would you solve similar equations with different constants (like 3.5 or 1.5)?
- What are some other common forms of equations that require finding the value of ?
Tip: Always check whether a constant multiplication in an equation can be simplified or factored out to make solving easier.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
General form of a linear equation: ax + b = c
Theorems
Properties of equality
Distributive property
Suitable Grade Level
Grades 8-10