a) \( 3 x+5=8 x-5 \)

To solve the equation \( 3x + 5 = 8x - 5 \), start by isolating the variable. First, subtract \( 3x \) from both sides: \( 5 = 5x - 5 \). Next, add \( 5 \) to both sides: \( 10 = 5x \). Finally, divide by \( 5 \) to get \( x = 2 \). Voila! You’ve found the value of \( x \). Now, you can easily check your solution by substituting \( x = 2 \) back into the original equation. Plugging it in gives you \( 3(2) + 5 = 8(2) - 5 \) which simplifies to \( 6 + 5 = 16 - 5 \). This results in \( 11 = 11 \), confirming that your answer is correct!