b) \( 5 x-12=8 \) \( 5 x=8+12 \) \( 5 x=20 \) \( x=\frac{20}{5}=4 \) c) \( 5 x-3=x+23 \)

To solve \( 5x - 3 = x + 23 \), start by getting all the terms involving \( x \) to one side. Subtract \( x \) from both sides to get \( 5x - x - 3 = 23 \), which simplifies to \( 4x - 3 = 23 \). Next, add 3 to both sides to isolate the term with \( x \): \( 4x = 26 \). Finally, divide both sides by 4, leading to \( x = \frac{26}{4} = 6.5 \). Now, double-check your solution by substituting \( x = 6.5 \) back into the original equation. On the left side, calculate \( 5(6.5) - 3 \) which equals \( 32.5 - 3 = 29.5 \). On the right side, substitute in \( 6.5 + 23 \) to find \( 29.5 \) as well. Perfect match! Always verify your findings, as it's a great way to catch a mistake or confirm your success.