text: ### Home > CCG > Chapter 12 > Lesson 12.2.1 > Problem12-65
  
  12-65.
  
  For each equation below, decide if the equation has any real number for the given variable. For each problem, explain how you know.
  
  1. $4\left(x-3\right)=11$
  
  Solve for $x$.
  Is your solution a real number?
  
  $\begin{array}{r} 4\left(x-3\right) = 11 \\ \div 4 \quad \div 4 \\ \hline x - 3 = \frac{11}{4} \\ x = \frac{23}{4} \end{array}$
  
  1. $x^2=-10$
  
  Is it possible for the square or absolute value of a number to be negative?
  
  No real solution, $x^2$ must be positive or zero.
  
  1. $3x^2-18=0$
  
  Refer to part (a) for help.
  
  1. $-7=\left|x-6\right|$
  
  Refer to part (b) for help.
explanation: The document contains a series of math problems and their solutions. Each problem asks whether a given equation has any real number solutions and provides an explanation or solution to determine this. The document includes both questions and answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ### Home > CCG > Chapter 12 > Lesson 12.2.1 > Problem12-65
  
  12-65.
  
  For each equation below, decide if the equation has any real number for the given variable. For each problem, explain how you know.
  
  1. $4\left(x-3\right)=11$
  
  Solve for $x$.
  Is your solution a real number?
  
  $\begin{array}{r} 4\left(x-3\right) = 11 \\ \div 4 \quad \div 4 \\ \hline x - 3 = \frac{11}{4} \\ x = \frac{23}{4} \end{array}$
  
  1. $x^2=-10$
  
  Is it possible for the square or absolute value of a number to be negative?
  
  No real solution, $x^2$ must be positive or zero.
  
  1. $3x^2-18=0$
  
  Refer to part (a) for help.
  
  1. $-7=\left|x-6\right|$
  
  Refer to part (b) for help.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a series of math problems and their solutions. Each problem asks whether a given equation has any real number solutions and provides an explanation or solution to determine this. The document includes both questions and answers.
  
  Label: multiple-question-and-answer