Question - Understanding Equation Solving With Like Terms
Solution:
To solve the equation $$ 403s + 1002s = 1410s $$, we can combine like terms on the left side by adding the coefficients of $$ s $$ together. Here's how you do it step by step:1. Combine like terms (the terms with $$ s $$):\[ 403s + 1002s = (403 + 1002)s = 1405s \]2. Now that we have $$ 1405s $$ on the left side and $$ 1410s $$ on the right side, we set them equal to each other:\[ 1405s = 1410s \]3. In order to find the solution for $$ s $$, you generally would isolate $$ s $$ by dividing both sides of the equation by the coefficient of $$ s $$. However, since the coefficients of $$ s $$ are equal and there is no constant term, this would result in an identity where any value of $$ s $$ satisfies the equation.But since the coefficients are actually different (1405 vs. 1410), there seems to be a mistake in the original problem or a transcription error. If the equation were correctly stated as $$ 1405s = 1410s $$, the only solution would be $$ s = 0 $$ because that would be the only way the two sides could be equal. Any non-zero value of $$ s $$ would result in the two sides not being equal.Since the equation you provided is already balanced with $$ 403s + 1002s = 1410s $$, which simplifies to $$ 1405s = 1410s $$, this equation has no solution for $$ s $$ unless there is a mistake in the terms provided. If the equation is correct, then the solution is that there is no value for $$ s $$ that would satisfy this equation.
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