(5) To find the value of \( r \), Stephen rewrites \( 3 r-18=27 \) as \( 3 i r-61=319 \). How could this help Stephen reason about the value of \( r \) ? Explain your reasoning. solution
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By rewriting the equation \( 3 r - 18 = 27 \) into \( 3 i r - 61 = 319 \), Stephen introduces an alternative perspective on the relationship between \( r \) and the constants involved. This new format allows Stephen to explore how different variables and constants interact, which could lead to discovering patterns or solutions that weren't as clear in the original equation. Essentially, it's about transforming a familiar problem into a new frame that might unveil hidden insights! Furthermore, this method can help Stephen visualize the changes in the equation. If he understands how altering coefficients and constants affects the outcome, he might be able to manipulate the expression more readily in future problems. Such thinking can foster mathematical flexibility, making it easier to tackle more complex equations down the road!