Math Problem Statement

Solve the equation: sqrt(2x) + 3 = 9

Solution

The equation displayed in the image is:

2x+3=9\sqrt{2x} + 3 = 9

Let's solve this step by step.

Step 1: Isolate the square root term.

To do this, subtract 3 from both sides of the equation:

2x=93\sqrt{2x} = 9 - 3 2x=6\sqrt{2x} = 6

Step 2: Square both sides.

Next, square both sides of the equation to eliminate the square root:

(2x)2=62(\sqrt{2x})^2 = 6^2 2x=362x = 36

Step 3: Solve for xx.

Now, divide both sides by 2:

x=362x = \frac{36}{2} x=18x = 18

Thus, the solution is x=18x = 18.

Would you like more details or have any questions about the steps? Here are some related questions you might find interesting:

  1. How do you handle equations with multiple square root terms?
  2. What happens if the equation involves a negative square root?
  3. Can you explain why squaring both sides is valid in algebraic manipulation?
  4. What would change if the equation had a cube root instead?
  5. How can you verify the solution after solving the equation?

Tip: Always check your final solution by substituting it back into the original equation to ensure it works correctly!

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Root Equations

Formulas

sqrt(a) = b -> a = b^2
Basic algebraic manipulation

Theorems

Properties of square roots
Basic algebraic theorems for solving linear equations

Suitable Grade Level

Grades 7-9