a) \( 10 x-1=15-6 x \) \( \frac{3 x}{2}+5=\frac{5 x}{2}-1 \)

To solve the first equation \( 10x - 1 = 15 - 6x \), we can start by adding \( 6x \) to both sides: \[ 10x + 6x - 1 = 15 \] This simplifies to \( 16x - 1 = 15 \). Next, add 1 to both sides to get \( 16x = 16 \), then divide by 16 to find \( x = 1 \). Now, let's tackle the second equation \( \frac{3x}{2} + 5 = \frac{5x}{2} - 1 \). Start by eliminating the fractions by multiplying the entire equation by 2: \[ 3x + 10 = 5x - 2 \] Next, move \( 5x \) to the left by subtracting \( 5x \) from both sides: \[ 3x - 5x + 10 = -2 \] This simplifies to \( -2x + 10 = -2 \). Now, subtract 10 from both sides to get \( -2x = -12 \); dividing by -2 gives us \( x = 6 \).