## Thinking Mathematically (6th Edition)

$\frac{x}{4}$ - $\frac{x}{5}$ =1 Step 1 : Multiply both the sides by 20 ($\frac{x}{4}$ - $\frac{x}{5}$)* 20 =1*20 Solve $\frac{x}{4}$*20 - $\frac{x}{5}$ * 20=1*20 5x - 4x = 20 Step 2 : Subtract 5x -4x = x x = 20 Now we check the proposed solution, 20 , by replacing x with 20 in the original equation. Step 1: the original equation $\frac{x}{4}$ - $\frac{x}{5}$ =1 Step2: Substitute 20 for x $\frac{20}{4}$ - $\frac{20}{5}$ =1 Step 3: Divide $\frac{20}{4}$ = 5, $\frac{20}{5}$ = 4 5 -4 =1 Step 4 : Subtract 5 - 4 =1 1= 1 Since the check results in true statement, we conclude that the solution set of the given equation is {20}.