Answer :
Let's analyze the given expression [tex]\(2x + 7\)[/tex].
1. Identify the variable and constants:
- In the expression [tex]\(2x + 7\)[/tex], [tex]\(x\)[/tex] is the variable.
- The term [tex]\(2x\)[/tex] consists of the coefficient [tex]\(2\)[/tex] (a constant) and the variable [tex]\(x\)[/tex].
- The term [tex]\(7\)[/tex] is also a constant.
2. Evaluate the statements:
- Statement (i) Variable [tex]\(= x\)[/tex], Constant [tex]\(=2\)[/tex]:
This statement is analyzing the term [tex]\(2x\)[/tex]. Here, [tex]\(x\)[/tex] is the variable, and [tex]\(2\)[/tex] is the coefficient (which is a constant). Thus, this statement is true.
- Statement (ii) Variable [tex]\(= x\)[/tex], Constant [tex]\(= 7\)[/tex]:
This statement is considering the entire expression. Here, [tex]\(x\)[/tex] remains the variable, and [tex]\(7\)[/tex] is a constant term. Thus, this statement is also true.
- Statement (iii) Variable [tex]\(= 7\)[/tex], Constant [tex]\(= x\)[/tex]:
This statement suggests [tex]\(7\)[/tex] should be treated as a variable and [tex]\(x\)[/tex] as a constant. In our context, this is incorrect because [tex]\(7\)[/tex] is clearly a constant term and [tex]\(x\)[/tex] is the variable. Thus, this statement is false.
3. Select the correct options:
Given the evaluations above:
- Statements (i) and (ii) are true.
- Statement (iii) is false.
Therefore, the correct option is:
c. (i) and (ii)
1. Identify the variable and constants:
- In the expression [tex]\(2x + 7\)[/tex], [tex]\(x\)[/tex] is the variable.
- The term [tex]\(2x\)[/tex] consists of the coefficient [tex]\(2\)[/tex] (a constant) and the variable [tex]\(x\)[/tex].
- The term [tex]\(7\)[/tex] is also a constant.
2. Evaluate the statements:
- Statement (i) Variable [tex]\(= x\)[/tex], Constant [tex]\(=2\)[/tex]:
This statement is analyzing the term [tex]\(2x\)[/tex]. Here, [tex]\(x\)[/tex] is the variable, and [tex]\(2\)[/tex] is the coefficient (which is a constant). Thus, this statement is true.
- Statement (ii) Variable [tex]\(= x\)[/tex], Constant [tex]\(= 7\)[/tex]:
This statement is considering the entire expression. Here, [tex]\(x\)[/tex] remains the variable, and [tex]\(7\)[/tex] is a constant term. Thus, this statement is also true.
- Statement (iii) Variable [tex]\(= 7\)[/tex], Constant [tex]\(= x\)[/tex]:
This statement suggests [tex]\(7\)[/tex] should be treated as a variable and [tex]\(x\)[/tex] as a constant. In our context, this is incorrect because [tex]\(7\)[/tex] is clearly a constant term and [tex]\(x\)[/tex] is the variable. Thus, this statement is false.
3. Select the correct options:
Given the evaluations above:
- Statements (i) and (ii) are true.
- Statement (iii) is false.
Therefore, the correct option is:
c. (i) and (ii)
