Find all real solutions for x:
\$\sqrt(5x - 3) = x - 2\$

A) \$x = (9 + \sqrt53)/2\$

B) \$x = (9 + \sqrt53)/3\$

C) \$x = (3 + \sqrt53)/2\$

D) \$x = (3 - \sqrt53)/2\$

Determine y such that:
\$root(3)(2y + 1) = root(3)(y - 1)\$

A) y = 3

B) y = - 2

C) y = 1

D) y = - 4

Solve for z and verify your solutions:
\$\sqrt(3z + 7) = z + 1\$

A) z = 2

B) z = 4

C) z = 3

D) z = 36

Find the value of w where: \$root(3)(w + 8) = root(3)(2w - 3)\$

A) w = 0

B) w = 9

C) w = 26

D) w = 11

Solve the equation for x:
\$\sqrt(2x^2 + 4) = x + 2\$

A) x = 1, 4

B) x = 2, 6

C) x = 0, 6

D) x = 0, 4

Identify v such that:
\$root(3)(4v + 5) = root(3)(v - 2)\$

A) \$- 2/5\$

B) 3.7

C) \$- 7/3\$

D) \$- 6/7\$

Find s for the following equation:
\$sqrt(3s + 7) = \sqrt(s - 1)\$

A) 2

B) - 4

C) - 7

D) 14

Determine the solutions to the equation:
\$\sqrt(4m + 1) = 2m - 3\$

A) \$2 + \sqrt(2)\$

B) \$2 + \sqrt(3)\$

C) \$2 - \sqrt(3)\$

D) \$3 - \sqrt(2)\$

Solve the equation and check all solutions:
\$root(3)(d^2 - 3d + 1)^3 = d - 1\$

A) \$d = - 2 + \sqrt(2), d = - 2 - \sqrt(2)\$

B) \$d = 2 + \sqrt(2), d = 2 - \sqrt(2)\$

C) \$d = 1 + \sqrt(2), d = 1 - \sqrt(2)\$

D) \$d = - 1 + \sqrt(2), d = - 1 - \sqrt(2)\$

Solve the equation: \$sqrt(5p^2 - 4p + 1) = p + 2\$

A) \$ p = (5 pm \sqrt2)/3\$

B) \$ p = (7 pm \sqrt7)/2\$

C) \$ p = (2 pm \sqrt7)/2\$

D) \$ p = (3 pm \sqrt5)/2\$