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g. \( \frac{10}{2 x-1}=8 \)

Ask by Gross Hamilton. in the United States
Mar 16,2025

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\( x = \frac{9}{8} \)

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To solve the equation \( \frac{10}{2 x-1} = 8 \), start by cross-multiplying to eliminate the fraction. This gives you \( 10 = 8(2x - 1) \). Expanding the right side results in \( 10 = 16x - 8 \). Next, add 8 to both sides, yielding \( 18 = 16x \). Finally, divide both sides by 16 to isolate \( x \), giving you \( x = \frac{18}{16} = \frac{9}{8} \). Double-checking solutions is key! After all the hard work of solving, it's easy to skip the final confirmation step. Plugging \( x = \frac{9}{8} \) back into the original equation gives \( \frac{10}{2(\frac{9}{8})-1} = \frac{10}{\frac{18}{8}-1} = \frac{10}{\frac{10}{8}} = 8\), confirming your solution is correct. Always a good practice—math can be tricky, and mistakes can slip in easily!

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