Question
What is the first step in solving the equation below? \( \sqrt{x-7}=\sqrt{9 x} \) Add 7 to both sides. square both sides. subtract \( 9 \times \) from both sides. Divide both sides by 9 .
Ask by Coleman Ramos. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The first step is to square both sides.
Solution
To solve the equation \( \sqrt{x-7}=\sqrt{9 x} \), the first step is to **square both sides**. This is because squaring both sides will eliminate the square roots, allowing us to work with a simpler equation.
So, the correct first step is to **square both sides**.
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Simplify this solution Beyond the Answer
To tackle this equation, the first step involves squaring both sides. Why? Because taking the square root of both sides typically eliminates the radical, simplifying your calculation. So, you'll square \( \sqrt{x-7} \) to get \( x-7 \), and square \( \sqrt{9x} \) to get \( 9x \). Easy-peasy, right? Now, if you were to add 7 to both sides first, you'd be putting that radical off for later. This may seem tempting, but remember to deal with those square roots early on for a smoother ride through the problem. Getting all the terms squared right away saves time and effort!
