Question 8 Solve the equation: \( \sqrt{x+1}+1=10 \) Answer: \( x=\square \) Question Help: Video

To solve the equation \( \sqrt{x+1}+1=10 \), first, isolate the square root by subtracting 1 from both sides. This gives us \( \sqrt{x+1} = 9 \). Next, square both sides to eliminate the square root, resulting in \( x + 1 = 81 \). Finally, subtract 1 from both sides to find \( x = 80 \). So, the solution is \( x = 80 \). Did you know that squaring both sides can sometimes introduce extraneous solutions? Always remember to plug your solution back into the original equation to ensure it fits. In our case, substituting \( x = 80 \) yields a true statement \( \sqrt{80 + 1} + 1 = 10 \). Equations like these are more than just math exercises; they represent real-world problems! For instance, think of the equation as an obstacle to reach a goal. The square root could represent a financial constraint you're trying to overcome—once you isolate and solve, you're on your way to achieving that target!