Answer :
Let's match each given description of an algebraic expression with the correct symbolic form step by step:
### Description 1:
2 terms; variable [tex]\(x\)[/tex], constant [tex]\(4.5\)[/tex]
To satisfy this description, we need an expression that has exactly two terms: one term involving the variable [tex]\(x\)[/tex] and one term that is a constant [tex]\(4.5\)[/tex].
Based on the given options:
- [tex]\( 4.5 - 2x \)[/tex]: This expression has two terms: [tex]\( 4.5 \)[/tex] (constant) and [tex]\( -2x \)[/tex] (term involving [tex]\(x\)[/tex]).
Thus, the matching expression is:
[tex]\[ \boxed{4.5 - 2x} \][/tex]
### Description 2:
2 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]
To satisfy this description, the expression should contain two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Based on the given options:
- None of the given expressions directly fit this description because they all have additional constants or more terms.
Thus, the matching expression is:
[tex]\[ \boxed{\text{Unable to determine with given data}} \][/tex]
### Description 3:
3 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]; constant [tex]\(3\)[/tex]
To satisfy this description, the expression should contain exactly three terms: two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and one term that is a constant [tex]\(3\)[/tex].
Based on the given options:
- [tex]\( x - 2y + 3 \)[/tex]: This expression has three terms: [tex]\( x \)[/tex] (term involving [tex]\(x\)[/tex]), [tex]\( -2y \)[/tex] (term involving [tex]\(y\)[/tex]), and [tex]\( +3 \)[/tex] (constant term).
Thus, the matching expression is:
[tex]\[ \boxed{x - 2y + 3} \][/tex]
### Description 4:
3 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]; constant [tex]\(2\)[/tex]
To satisfy this description, the expression should contain exactly three terms: two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and one term that is a constant [tex]\(2\)[/tex].
Based on the given options:
- [tex]\( 4.5x + 2 - 3y \)[/tex]: This expression has three terms: [tex]\( 4.5x \)[/tex] (term involving [tex]\(x\)[/tex]), [tex]\( -3y \)[/tex] (term involving [tex]\(y\)[/tex]), and [tex]\( +2 \)[/tex] (constant term).
Thus, the matching expression is:
[tex]\[ \boxed{4.5x + 2 - 3y} \][/tex]
So, the final matching expressions are:
1. [tex]\( 2 \)[/tex] terms; variable [tex]\( x \)[/tex], constant [tex]\( 4.5 \)[/tex]: [tex]\( 4.5 - 2x \)[/tex]
2. [tex]\( 2 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]: Unable to determine with given data
3. [tex]\( 3 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( 3 \)[/tex]: [tex]\( x - 2y + 3 \)[/tex]
4. [tex]\( 3 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( 2 \)[/tex]: [tex]\( 4.5x + 2 - 3y \)[/tex]
### Description 1:
2 terms; variable [tex]\(x\)[/tex], constant [tex]\(4.5\)[/tex]
To satisfy this description, we need an expression that has exactly two terms: one term involving the variable [tex]\(x\)[/tex] and one term that is a constant [tex]\(4.5\)[/tex].
Based on the given options:
- [tex]\( 4.5 - 2x \)[/tex]: This expression has two terms: [tex]\( 4.5 \)[/tex] (constant) and [tex]\( -2x \)[/tex] (term involving [tex]\(x\)[/tex]).
Thus, the matching expression is:
[tex]\[ \boxed{4.5 - 2x} \][/tex]
### Description 2:
2 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]
To satisfy this description, the expression should contain two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Based on the given options:
- None of the given expressions directly fit this description because they all have additional constants or more terms.
Thus, the matching expression is:
[tex]\[ \boxed{\text{Unable to determine with given data}} \][/tex]
### Description 3:
3 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]; constant [tex]\(3\)[/tex]
To satisfy this description, the expression should contain exactly three terms: two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and one term that is a constant [tex]\(3\)[/tex].
Based on the given options:
- [tex]\( x - 2y + 3 \)[/tex]: This expression has three terms: [tex]\( x \)[/tex] (term involving [tex]\(x\)[/tex]), [tex]\( -2y \)[/tex] (term involving [tex]\(y\)[/tex]), and [tex]\( +3 \)[/tex] (constant term).
Thus, the matching expression is:
[tex]\[ \boxed{x - 2y + 3} \][/tex]
### Description 4:
3 terms; variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]; constant [tex]\(2\)[/tex]
To satisfy this description, the expression should contain exactly three terms: two terms involving the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and one term that is a constant [tex]\(2\)[/tex].
Based on the given options:
- [tex]\( 4.5x + 2 - 3y \)[/tex]: This expression has three terms: [tex]\( 4.5x \)[/tex] (term involving [tex]\(x\)[/tex]), [tex]\( -3y \)[/tex] (term involving [tex]\(y\)[/tex]), and [tex]\( +2 \)[/tex] (constant term).
Thus, the matching expression is:
[tex]\[ \boxed{4.5x + 2 - 3y} \][/tex]
So, the final matching expressions are:
1. [tex]\( 2 \)[/tex] terms; variable [tex]\( x \)[/tex], constant [tex]\( 4.5 \)[/tex]: [tex]\( 4.5 - 2x \)[/tex]
2. [tex]\( 2 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]: Unable to determine with given data
3. [tex]\( 3 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( 3 \)[/tex]: [tex]\( x - 2y + 3 \)[/tex]
4. [tex]\( 3 \)[/tex] terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( 2 \)[/tex]: [tex]\( 4.5x + 2 - 3y \)[/tex]
