Sure! Let's match each description of an algebraic expression with its corresponding symbolic form, step by step.
1. Description: 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=3$[/tex]
- Here, we need an expression that has exactly 3 terms, includes the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and has a constant term that equals 3.
- Matching Expression: [tex]\( x - 2y + 3 \)[/tex]
2. Description: 3 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]; constant [tex]$=2$[/tex]
- Here, we need an expression that also has exactly 3 terms, includes the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], and has a constant term that equals 2.
- Matching Expression: [tex]\( 4.5x + 2 - 3y \)[/tex]
3. Description: 2 terms; variable [tex]$=x$[/tex], constant [tex]$=4.5$[/tex]
- Here, we need an expression that has exactly 2 terms, includes the variable [tex]\( x \)[/tex], and has a constant term that equals 4.5.
- Matching Expression: [tex]\( 4.5 - 2x \)[/tex]
4. Description: 2 terms; variables [tex]$=x$[/tex] and [tex]$y$[/tex]
- Here, we need an expression that has exactly 2 terms and includes both variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- Matching Expression: [tex]\( 4.5y - 2x \)[/tex]
So, the final matches are:
- 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]
- 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] : [tex]\( 4.5y - 2x \)[/tex]
