Questions: Find all real solutions of the equation. 7 = √(3x - 2) x = □

Find all real solutions of the equation. 7 = √(3x - 2) x = □
Transcript text: Find all real solutions of the equation. \[ \begin{array}{l} 7=\sqrt{3 x-2} \\ x=\square \end{array} \]
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Solution

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Solution Steps

To find the real solutions of the equation \( 7 = \sqrt{3x - 2} \), we need to isolate \( x \). First, square both sides of the equation to eliminate the square root. Then, solve the resulting linear equation for \( x \).

Step 1: Isolate the Square Root

Given the equation: \[ 7 = \sqrt{3x - 2} \]

Step 2: Square Both Sides

Square both sides to eliminate the square root: \[ 7^2 = (\sqrt{3x - 2})^2 \] \[ 49 = 3x - 2 \]

Step 3: Solve for \( x \)

Rearrange the equation to solve for \( x \): \[ 49 + 2 = 3x \] \[ 51 = 3x \] \[ x = \frac{51}{3} \] \[ x = 17 \]

Final Answer

\(\boxed{x = 17}\)

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