(9) \( \frac{x}{5}+\frac{x}{3}-1=\frac{x}{2} \)
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Let's solve the equation \( \frac{x}{5}+\frac{x}{3}-1=\frac{x}{2} \). First, we need to find a common denominator for the fractions, which is 30. Rewriting each term: - \( \frac{x}{5} = \frac{6x}{30} \) - \( \frac{x}{3} = \frac{10x}{30} \) - \( \frac{x}{2} = \frac{15x}{30} \) Now, we can rewrite the equation: \[ \frac{6x}{30} + \frac{10x}{30} - 1 = \frac{15x}{30} \] Combining the terms on the left side gives us: \[ \frac{16x}{30} - 1 = \frac{15x}{30} \] Next, let's eliminate the fractions by multiplying through by 30: \[ 16x - 30 = 15x \] Now, isolate \( x \) by subtracting \( 15x \) from both sides: \[ 16x - 15x = 30 \] This simplifies to: \[ x = 30 \] Thus, the solution to the equation is \( x = 30 \).