Math Problem Statement

Solve for 

q

 in terms of 

p

,   r

,

 and 

s

.

r

=

p

q

s

Solution

To solve for qq in terms of pp, rr, and ss, start with the given equation:

r=p+qsr = p + q - s

Step-by-step solution:

  1. Add ss to both sides of the equation to isolate the terms with qq on one side: r+s=p+qr + s = p + q

  2. Subtract pp from both sides: r+sp=qr + s - p = q

Thus, the solution for qq in terms of pp, rr, and ss is: q=r+spq = r + s - p

Would you like any further details or have any questions about the solution?

Here are 5 related questions to explore:

  1. How would the solution change if the equation was r=p+q+sr = p + q + s?
  2. Can you rearrange the equation r=p+qsr = p + q - s to solve for pp instead of qq?
  3. What happens if s=0s = 0 in the original equation?
  4. If q=r+spq = r + s - p, what does qq represent geometrically?
  5. How do you solve the equation if all terms are squared?

Tip: Always check your final equation by substituting values back into the original to verify the correctness of your solution.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Rearranging Equations

Formulas

r = p + q - s
q = r + s - p

Theorems

Basic Algebraic Rearrangement

Suitable Grade Level

Grades 6-8