Solve.
StartRoot 3 x minus 5 EndRoot equals 4
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Part 1
Select the correct choice below and fill in any answer boxes present in your choice.
A.
x equals nothing
  
 
​(Simplify your answer. Use a comma to separate answers as​ needed.)
B.
There is no solution.

To solve the equation \( \sqrt{3x - 5} = 4 \), follow these steps:

1. **Square both sides** to eliminate the square root:
   \[
   (\sqrt{3x - 5})^2 = 4^2
   \]
   This simplifies to:
   \[
   3x - 5 = 16
   \]

2. **Add 5 to both sides**:
   \[
   3x = 16 + 5
   \]
   Simplifying gives:
   \[
   3x = 21
   \]

3. **Divide by 3**:
   \[
   x = \frac{21}{3}
   \]
   Simplifying further, we find:
   \[
   x = 7
   \]

Thus, the solution is:
**A. \( x = 7 \)**.

If you have any questions or need further details, let me know! Here are some related questions to consider:

1. What are the steps to check if the solution is correct?
2. How would the solution change if the equation was \( \sqrt{3x - 5} = -4 \)?
3. What is the importance of squaring both sides in equations involving square roots?
4. Can you provide another example of solving a square root equation?
5. What other methods can be used to solve equations involving square roots?

**Tip:** Always check your solution by substituting it back into the original equation to verify it satisfies the equation.

Solve. StartRoot 3 x minus 5 EndRoot equals 4

Discover how to solve the equation √(3x - 5) = 4 step-by-step. This guide explains the process of squaring both sides, simplifying the equation, and finding the solution x = 7. Ideal for students in Grades 7-9.

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