Sure, let's match each description of an algebraic expression with the given symbolic forms step-by-step:
1. Description: 2 terms; variable [tex]$=x$[/tex]; constant [tex]$=4.5$[/tex]
- Explanation: This description specifies an algebraic expression with 2 terms, involving a variable [tex]\( x \)[/tex] and a constant 4.5.
- Matching Expression: Among the given symbolic forms, the expression that fits this description is [tex]\( 4.5 - 2x \)[/tex] because:
- It has two terms: [tex]\( 4.5 \)[/tex] (constant term) and [tex]\(-2x\)[/tex] (variable term with [tex]\( x \)[/tex]).
Therefore, the match is:
- [tex]\( 4.5 - 2x \)[/tex]
2. Description: 2 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]
- Explanation: This description specifies an algebraic expression with 2 terms involving variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- Matching Expression: Based on the provided matches, there is no expression given that matches exactly this description.
Therefore, the match is:
- None
3. Description: 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=3$[/tex]
- Explanation: This description specifies an algebraic expression with 3 terms, involving variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and a constant value 3.
- Matching Expression: Among the given symbolic forms, the expression that fits this description is [tex]\( x - 2y + 3 \)[/tex] because:
- It has three terms: [tex]\( x \)[/tex] (variable term with [tex]\( x \)[/tex]), [tex]\(-2y \)[/tex] (variable term with [tex]\( y \)[/tex]), and [tex]\( 3 \)[/tex] (constant term).
Therefore, the match is:
- [tex]\( x - 2y + 3 \)[/tex]
4. Description: 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=2$[/tex]
- Explanation: This description specifies an algebraic expression with 3 terms, involving variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and a constant value 2.
- Matching Expression: Among the given symbolic forms, the expression that fits this description is [tex]\( 4.5x + 2 - 3y \)[/tex] because:
- It has three terms: [tex]\( 4.5x \)[/tex] (variable term with [tex]\( x \)[/tex]), [tex]\( -3y \)[/tex] (variable term with [tex]\( y \)[/tex]), and [tex]\( 2 \)[/tex] (constant term).
Therefore, the match is:
- [tex]\( 4.5x + 2 - 3y \)[/tex]
In conclusion, the matches are as follows:
- 2 terms; variable [tex]$=x$[/tex]; constant [tex]$=4.5$[/tex]: [tex]\( 4.5 - 2x \)[/tex]
- 2 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]: None
- 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=3$[/tex]: [tex]\( x - 2y + 3 \)[/tex]
- 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=2$[/tex]: [tex]\( 4.5x + 2 - 3y \)[/tex]
