Select the correct answer.
What is the solution to the equation?

A. -1 and 2
B. -2 and 1
C. 2
D. 1

Question

Select the correct answer. What is the solution to the equation? $$ \sqrt{3 x+3}-1=x $$ A. -1 and 2 B. -2 and 1 C. 2 D. 1

UpStudy AI · Accepted Answer

Solve the equation $$ \sqrt{3x+3}-1=x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\sqrt{3x+3}-1=x$$
- step1: Find the domain:
  $$\sqrt{3x+3}-1=x ,x\geq -1$$
- step2: Move the constant to the right-hand side:
  $$\sqrt{3x+3}=x+1$$
- step3: Evaluate:
  $$\sqrt{3x+3}=x+1,x+1\geq 0$$
- step4: Evaluate:
  $$\sqrt{3x+3}=x+1,x\geq -1$$
- step5: Solve the equation:
  $$\begin{align}&x=2\&x=-1\end{align},x\geq -1$$
- step6: Find the intersection:
  $$\begin{align}&x=2\&x=-1\end{align}$$
- step7: Check the solution:
  $$\begin{align}&x=2\&x=-1\end{align}$$
- step8: Rewrite:
  $$x_{1}=-1,x_{2}=2$$
The solution to the equation $$ \sqrt{3x+3}-1=x $$ is $$ x=-1 $$ and $$ x=2 $$.

Therefore, the correct answer is:
A. -1 and 2
The solution is $$ x=-1 $$ and $$ x=2 $$, so the correct answer is A.

Select the correct answer.
What is the solution to the equation?

A. -1 and 2
B. -2 and 1
C. 2
D. 1

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Solución

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Select the correct answer.
What is the solution to the equation?

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B. -2 and 1
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