Let's break down the problem step by step:
Step 1: Understanding the expression
The expression [tex]\( x + x + 10 + 2x - 16 \)[/tex] represents the combined golf scores of Erick, Mia, and Isabelle. Specifically:
- [tex]\( x \)[/tex] is Mia’s score.
- [tex]\( x + 10 \)[/tex] is Erick’s score because he scored 10 more than Mia.
- [tex]\( 2x - 16 \)[/tex] is Isabelle’s score because she scored 16 less than twice Mia's score.
Thus, the expression [tex]\( x + x + 10 + 2x - 16 \)[/tex] represents the total score contributed by Mia, Erick, and Isabelle.
Step 2: Identifying the variable in the expression
The variable [tex]\( x \)[/tex] represents Mia's score.
Step 3: Simplifying the expression
To simplify the expression:
[tex]\[ x + x + 10 + 2x - 16 \][/tex]
- Combine the like terms involving [tex]\( x \)[/tex]:
[tex]\[ x + x + 2x = 4x \][/tex]
- Combine the constant terms:
[tex]\[ 10 - 16 = -6 \][/tex]
So, the simplified form of the expression becomes:
[tex]\[ 4x - 6 \][/tex]
Step 4: Identifying the constant in the simplified expression
In the simplified expression [tex]\( 4x - 6 \)[/tex], the constant term is [tex]\(-6\)[/tex].
Therefore, the completed statements should be:
- The expression [tex]\( x + x + 10 + 2x - 16 \)[/tex] represents the combined scores of Erick, Mia, and Isabelle.
- The variable in the expression, [tex]\( x \)[/tex], represents Mia's score.
- The expression in simplified form is [tex]\( 4x - 6 \)[/tex].
- The constant in the simplified expression is [tex]\(-6\)[/tex].
