a) \( 3 x+2-x<5 x+17 \)

To solve the inequality \( 3x + 2 - x < 5x + 17 \), first, simplify the left side. Combine like terms: \( 3x - x = 2x \), so the inequality becomes \( 2x + 2 < 5x + 17 \). Next, isolate the variable by subtracting \( 2x \) from both sides: \( 2 < 3x + 17 \). Then, subtract \( 17 \) from both sides to get \( -15 < 3x \). Finally, divide by \( 3 \) to find \( -5 < x \) or equivalently, \( x > -5 \). To check if your solution is accurate, plug in a number greater than \(-5\) into the original inequality. For example, if you try \(x = 0\), substituting gives you \(2 < 17\), which is true! This affirms that the solution \(x > -5\) is indeed correct.