Sure, let's match each description of an algebraic expression with its symbolic form step-by-step.
1. Description: "2 terms; variable [tex]\( x \)[/tex], constant [tex]\( 4.5 \)[/tex]"
- Here, we have an algebraic expression with exactly two terms.
- One term involves the variable [tex]\( x \)[/tex], and the other term is a constant which is [tex]\( 4.5 \)[/tex].
- The correct expression that matches this description is: [tex]\( 4.5 - 2x \)[/tex].
2. Description: "3 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( =2 \)[/tex]"
- This expression includes three terms.
- It has variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and a constant term that is [tex]\( 2 \)[/tex].
- The correct expression that matches this description is: [tex]\( 4.5x + 2 - 3y \)[/tex].
3. Description: "2 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]"
- This expression has exactly two terms.
- Both terms include variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- The correct expression that matches this description is: [tex]\( 4.5y - 2x \)[/tex].
4. Description: "3 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( =3 \)[/tex]"
- This expression includes three terms.
- It has variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and a constant term that equals [tex]\( 3 \)[/tex].
- The correct expression that matches this description is: [tex]\( x - 2y + 3 \)[/tex].
So, the matches for each description with the symbolic form of that expression are as follows:
1. "2 terms; variable [tex]\( x \)[/tex], constant [tex]\( 4.5 \)[/tex]" corresponds to [tex]\( 4.5 - 2x \)[/tex].
2. "3 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( =2 \)[/tex]" corresponds to [tex]\( 4.5x + 2 - 3y \)[/tex].
3. "2 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]" corresponds to [tex]\( 4.5y - 2x \)[/tex].
4. "3 terms; variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]; constant [tex]\( =3 \)[/tex]" corresponds to [tex]\( x - 2y + 3 \)[/tex].
