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How do you solve for r in \[p - r = r\] ?

Last updated date: 22nd Feb 2024
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IVSAT 2024
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Hint:To find the value of r, just isolate the terms with respect to the variable asked i.e., here in this question we need to add both sides of the expression by \[r\]and hence by solving this we can get the expression of r.

Complete step by step answer:
The given expression is
\[p - r = r\]
As we need to solve for r, hence rewriting the given expression as
\[r = p - r\]
Now add both sides of the expression by \[r\] as
\[r + r = p - r + r\]
The obtained expression consists of common terms i.e., -r and +r is common and implies to zero, hence by simplifying the terms we get
\[r + r = p\]
\[2r = p\]
Divide the expression by 2, to get the term r as
\[\dfrac{{2r}}{2} = \dfrac{p}{2}\]
Hence, the expression implies to
\[r = \dfrac{p}{2}\]
Therefore, the expression of r is \[r = \dfrac{p}{2}\]
Additional information: We have 4 ways of solving one-step equations: Adding, Subtracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal.

Note: The key point to find the value of variable asked is Isolate r on one side of the algebraic equation by subtracting the sum that appears on the same side of the equation as the r and that equals sign verifies the condition that the inherent value on the left is the same as the inherent value on the right. So, what you do to one side you also have to do to the right. Otherwise, one side is not the same value as the other.