\( 10 x-1=15-6 x \)
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To solve the equation \( 10x - 1 = 15 - 6x \), we first want to get all the \( x \) terms on one side and the constant terms on the other. We can do this by adding \( 6x \) to both sides, which gives us \( 10x + 6x - 1 = 15 \). Simplifying this, we find \( 16x - 1 = 15 \). Next, add \( 1 \) to both sides to obtain \( 16x = 16 \). Finally, divide by \( 16 \) to isolate \( x \); thus, \( x = 1 \). To check our work, we can substitute \( x = 1 \) back into the original equation. \( 10(1) - 1 = 15 - 6(1) \) simplifies to \( 9 = 9 \), confirming our solution is correct!