Question

solve for v, where v is a real number.\\(\sqrt{9 - 5v} = 7\\)\
if there is more than one solution, separate them with commas.\
if there is no solution, click on
o solution\.\
v = \boxed{}

Explanation:

Step1: Square both sides to eliminate root

$$(\sqrt{9-5v})^2 = 7^2$$
$$9-5v = 49$$

Step2: Isolate the variable term

$$-5v = 49 - 9$$
$$-5v = 40$$

Step3: Solve for v

$$v = \frac{40}{-5}$$
$$v = -8$$

Step4: Verify the solution

Substitute $v=-8$ into original equation:
$$\sqrt{9-5(-8)} = \sqrt{9+40} = \sqrt{49} = 7$$
This matches the right-hand side, so the solution is valid.

Answer:

$v = -8$