Question: $$2 x + 5 = 3 x + 2$$

Solution

Step 1: Subtract \(2x\) from both sides of the equation. \[ 2x + 5 = 10x + 1 & \] \[ 2x + 5 - 2x = 10x + 1 - 2x & \] Step 2: Simplify both sides of the equation. \[ 5 = 8x + 1 & \] Step 3: Subtract \(1\) from both sides to isolate the term with \(x\). \[ 5 - 1 = 8x + 1 - 1 & \] \[ 4 = 8x & \] Step 4: Divide both sides by \(8\) to solve for \(x\). \[ \frac{4}{8} = \frac{8x}{8} & \] \[ 0.5 = x & \] So, the solution is \(x = 0.5\).