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.