Question

1. solve for x: (sqrt{x - 7} - 10 = -9)

Explanation:

Step1: Isolate the square root term

Add 10 to both sides of the equation to isolate the square root.
$\sqrt{x - 7} - 10 + 10 = -9 + 10$
$\sqrt{x - 7} = 1$

Step2: Eliminate the square root

Square both sides of the equation to eliminate the square root.
$(\sqrt{x - 7})^2 = 1^2$
$x - 7 = 1$

Step3: Solve for x

Add 7 to both sides of the equation.
$x - 7 + 7 = 1 + 7$
$x = 8$

Step4: Check the solution

Substitute $x = 8$ back into the original equation:
Left side: $\sqrt{8 - 7} - 10 = \sqrt{1} - 10 = 1 - 10 = -9$
Right side: $-9$
Since both sides are equal, $x = 8$ is a valid solution.

Answer:

$x = 8$