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:

2.5(yx)=02.5(y - x) = 0

And we're told that when the solution is y=6y = 6, we need to find what must be true about xx.

Step 1: Analyze the equation

The given equation is:

2.5(yx)=02.5(y - x) = 0

Since we know y=6y = 6, substitute y=6y = 6 into the equation:

2.5(6x)=02.5(6 - x) = 0

Step 2: Solve for xx

Now simplify the equation:

6x=06 - x = 0

Solving for xx, we find:

x=6x = 6

Conclusion:

For the equation 2.5(yx)=02.5(y - x) = 0 to hold true with y=6y = 6, the value of xx must also be 66.

Justification:

The equation 2.5(yx)=02.5(y - x) = 0 implies that (yx)(y - x) must be zero because multiplying by 2.5 doesn't affect the equality. Thus, for y=6y = 6, we must have 6x=06 - x = 0, which leads to x=6x = 6.


Would you like more details on the steps or any clarification? Here are some related questions:

  1. What happens to the equation if y6y \neq 6?
  2. How does multiplying an equation by a constant affect its solution?
  3. What other equations would have the same solution for xx?
  4. How would you solve similar equations with different constants (like 3.5 or 1.5)?
  5. What are some other common forms of equations that require finding the value of xx?

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