Question

\\\sqrt{2x + 3} + 2 = 7\\

Explanation:

Isolate the radical term

Subtract \(2\) from both sides.

$$ \sqrt{2x + 3} = 7 - 2 $$

$$ \sqrt{2x + 3} = 5 $$

Square both sides

Eliminate the square root.

$$ (\sqrt{2x + 3})^2 = 5^2 $$

$$ 2x + 3 = 25 $$

Solve for x

Subtract \(3\) and divide.

$$ 2x = 22 $$

$$ x = 11 $$

Verify the solution

Check the original equation.

$$ \sqrt{2(11) + 3} + 2 = \sqrt{25} + 2 = 5 + 2 = 7 $$

Answer:

\(x = 11\)