Question

this is an example of an sat/tsi questions. no graphing allowed.
if $sqrt{x+z}=sqrt{3x+10}$, find the solution if the value of $z=8$.
$circ x=3$
$circ x=-1$
$circ x=-2$
$circ x=5$

Explanation:

Step1: Substitute z=8 into equation

$\sqrt{x + 8} = \sqrt{3x + 10}$

Step2: Square both sides to eliminate roots

$(\sqrt{x + 8})^2 = (\sqrt{3x + 10})^2$
$x + 8 = 3x + 10$

Step3: Rearrange to solve for x

$8 - 10 = 3x - x$
$-2 = 2x$
$x = \frac{-2}{2} = -1$

Step4: Verify solution (ensure non-negative roots)

Left side: $\sqrt{-1 + 8} = \sqrt{7}$
Right side: $\sqrt{3(-1) + 10} = \sqrt{7}$
Both sides are valid.

Answer:

B. x = -1