Question

solve.
\sqrt{7x} = 7

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution(s) is(are) x = \square.
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

b. there is no solution.

Explanation:

Step1: Square both sides to eliminate the square root

To solve the equation \(\sqrt{7x} = 7\), we first square both sides of the equation. Squaring a square root cancels out the square root operation. So, we have:
\[
(\sqrt{7x})^2 = 7^2
\]
Simplifying both sides, the left side becomes \(7x\) (because squaring the square root of \(7x\) gives \(7x\)) and the right side is \(49\) (since \(7^2 = 49\)). So the equation simplifies to:
\[
7x = 49
\]

Step2: Solve for \(x\)

Now we solve for \(x\) by dividing both sides of the equation \(7x = 49\) by \(7\). Dividing both sides by the coefficient of \(x\) (which is \(7\)) will isolate \(x\). So we have:
\[
x = \frac{49}{7}
\]
Simplifying the right side, \(\frac{49}{7} = 7\). We should also check if this solution is valid by plugging it back into the original equation. Substituting \(x = 7\) into \(\sqrt{7x}\), we get \(\sqrt{7\times7} = \sqrt{49} = 7\), which matches the right side of the original equation. So \(x = 7\) is a valid solution.

Answer:

A. The solution(s) is(are) \(x = 7\)