Solve the following inequality: \( 3 x+2<5 x-1 \)

To solve the inequality \( 3x + 2 < 5x - 1 \), let's start by isolating the variable \( x \). First, subtract \( 3x \) from both sides: \[ 2 < 5x - 3x - 1 \] This simplifies to: \[ 2 < 2x - 1 \] Next, add \( 1 \) to both sides: \[ 2 + 1 < 2x \] Which gives us: \[ 3 < 2x \] Now, divide both sides by \( 2 \): \[ \frac{3}{2} < x \] Or, rewriting it, we have: \[ x > \frac{3}{2} \] So the solution to the inequality is \( x > \frac{3}{2} \). This means any value greater than \( 1.5 \) will satisfy the original inequality!