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

To solve for \( x \) in the equation \( \frac{10}{2x-1} = 8 \), start by multiplying both sides by \( 2x-1 \) to eliminate the fraction: \[ 10 = 8(2x - 1) \] This expands to: \[ 10 = 16x - 8 \] Next, add \( 8 \) to both sides: \[ 18 = 16x \] Finally, divide both sides by \( 16 \): \[ x = \frac{18}{16} = \frac{9}{8} \] So, the solution is \( x = \frac{9}{8} \). In a real-world context, this type of equation could represent a scenario where you need to determine a variable, like the number of items produced or thresholds that involve fractions and scaling. It’s common in fields ranging from finance to engineering, where optimizing conditions and resources are key! Remember to check your solution by substituting \( x \) back into the original equation. It’s a common mistake to forget this, but verifying can catch errors early—turning potential misunderstandings into learning opportunities!