What is the solution of [tex]\(\sqrt{1-3x} = x + 3\)[/tex]?

A. [tex]\(x = -8\)[/tex] or [tex]\(x = -1\)[/tex]
B. [tex]\(x = -8\)[/tex]
C. [tex]\(x = -1\)[/tex]
D. No solution



Answer :

To solve the equation [tex]\(\sqrt{1-3x} = x + 3\)[/tex], we'll follow a step-by-step approach to verify the given possible solutions: [tex]\(x = -8\)[/tex] and [tex]\(x = -1\)[/tex].

1. Test [tex]\( x = -8 \)[/tex] in the original equation:
[tex]\[ \sqrt{1-3(-8)} = -8 + 3 \][/tex]
Simplify inside the square root:
[tex]\[ \sqrt{1 + 24} = -5 \][/tex]
This reduces to:
[tex]\[ \sqrt{25} = -5 \][/tex]
which simplifies to:
[tex]\[ 5 \neq -5 \][/tex]
The solution [tex]\( x = -8 \)[/tex] does not satisfy the original equation.

2. Test [tex]\( x = -1 \)[/tex] in the original equation:
[tex]\[ \sqrt{1-3(-1)} = -1 + 3 \][/tex]
Simplify inside the square root:
[tex]\[ \sqrt{1 + 3} = 2 \][/tex]
This reduces to:
[tex]\[ 2 = 2 \][/tex]
The solution [tex]\( x = -1 \)[/tex] satisfies the original equation.

Therefore, among the given solutions [tex]\( x = -8 \)[/tex] and [tex]\( x = -1 \)[/tex], the only correct solution is [tex]\( x = -1 \)[/tex].

So the solution of [tex]\(\sqrt{1-3x} = x+3\)[/tex] is:
[tex]\[ \boxed{x = -1} \][/tex]