Solve the following equation \$\sqrt(3x + 7) - x = 3\$.

Given equation

\$\sqrt(3x + 7) - x = 3\$

Add x to both sides to isolate the square root term

\$\sqrt(3x + 7) - x + x = 3 + x\$

\$\sqrt(3x + 7) = 3 + x\$

Square both sides of the equation

\$(\sqrt(3x + 7))^2 = (3 + x)^2\$

\$(3x + 7) = (3 + x)(3 + x)\$

3x + 7 = \$x^2 + 6x + 9\$

Move all terms to one side to set the equation to zero

\$0 = x^2 + 6x + 9 - 3x - 7\$

\$0 = x^2 + 3x + 2\$

Factor the quadratic equation Set each factor equal to zero and solve for x:

0 = (x + 1)(x + 2)

x + 1 = 0

x = -1

x + 2 = 0

x = -2

Check both solutions in the original equation to ensure they are valid: For x = -1:

\$\sqrt(3(-1) + 7) - (-1) = 3\$

\$\sqrt4 + 1 = 3\$

2 + 1 = 3

3 = 3

For x = -2:

\$\sqrt(3(-2) + 7) - (-2) = 3\$

\$\sqrt1 + 2 = 3\$

1 + 2 = 3

3 = 3

Therefore, the solutions to the equation \$\sqrt(3x + 7) - x = 3 \$ are x = -1, -2.

This option is correct because it includes values of x that satisfy the equation \$\sqrt(3x + 7) - x = 3\$, namely x = -1 and x = -2

(x = -1, -2)

This option is not correct because it includes values of x that do not satisfy the equation \$\sqrt(3x + 7) - x = 3\$

(x = 1, -4)

This option is not correct because it suggests only one value of x that does not satisfy the equation \$\sqrt(3x + 7) - x = 3\$

x = 25

This option is not correct because it includes a value of x that does not satisfy the equation \$\sqrt(3x + 7) - x = 3\$

(x = -7)

Option

A

Can you summarize what you’ve understood in the above steps?