Some algebra I don't understand: Solve for R

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    Algebra Algebra i
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Homework Help Overview

The discussion revolves around solving the equation for the variable R, specifically the equation $$\frac{5}{3} = \frac{0.28 + R}{R}$$. Participants express uncertainty about the steps needed to isolate R and address the presence of R in multiple terms.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest various methods to manipulate the equation, such as multiplying both sides by R or a common denominator to eliminate fractions. There is discussion about merging or eliminating R terms and simplifying the equation.

Discussion Status

The conversation includes multiple perspectives on how to approach the problem, with some participants offering different algebraic manipulations. There is no explicit consensus on the best method, but several productive suggestions have been made regarding how to handle the equation.

Contextual Notes

Some participants note that R appears in multiple places within the equation, which adds to the complexity of the problem. There is also a mention of the original poster's confusion regarding the isolation of R.

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Homework Statement
Solve for R. $$\frac{5}{3} = \frac{0.28 + R}{R}$$
Relevant Equations
Use algebra I guess
The variable is already isolated on one side. I dont' know how to solve for R though. Any help? Thank you.
 
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Jaccobtw said:
Homework Statement:: Solve for R. $$\frac{5}{3} = \frac{0.28 + R}{R}$$
Relevant Equations:: Use algebra I guess

The variable is already isolated on one side. I dont' know how to solve for R though. Any help? Thank you.
Fractions are always a problem. Get rid of them!
 
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PeroK said:
Fractions are always a problem. Get rid of them!
Ah ok. Multiply both sides by R and then subtract R from both sides. The rest is cake
 
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Jaccobtw said:
Ah ok. Multiply both sides by R and then subtract R from both sides. The rest is cake
Better yet, multiply both sides of the equation by 3R, and then isolate the terms with R on one side.
 
the difficulty here is R appears twice
we can either merge the R's or eliminate one
to do the later we can...

subtract one from both sides
$$\frac{5}{3} = \frac{0.28 + R}{R}$$
$$\frac{5}{3} -\frac{3}{3}= \frac{0.28 + R}{R}-\frac{R}{R}$$
 
Jaccobtw said:
Homework Statement:: Solve for R. $$\frac{5}{3} = \frac{0.28 + R}{R}$$
Relevant Equations:: Use algebra I guess

The variable is already isolated on one side. I dont' know how to solve for R though. Any help? Thank you.
Although R is only on the right-side, I would not describe that R as "isolated".

lurflurf said:
the difficulty here is R appears twice
we can either merge the R's or eliminate one
to do the later we can...

subtract one from both sides
$$\frac{5}{3} = \frac{0.28 + R}{R}$$
$$\frac{5}{3} -\frac{3}{3}= \frac{0.28 + R}{R}-\frac{R}{R}$$
While true, it may be better to simplify [to reduce the number of R's one sees on]
the right-hand-side by first distributing the [common] denominator, then simplifying further
$$\begin{align*}\frac{5}{3}
&=
\frac{0.28 + R}{R}\\
&=
\frac{0.28}{R} + 1\\
\end{align*}
$$
 
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