### 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.
The text contains a series of mathematical problems, each followed by a question about the existence of real number solutions and an explanation or solution.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
### 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.
user
The text contains a series of mathematical problems, each followed by a question about the existence of real number solutions and an explanation or solution.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS