Sure, let's look at each part of the question and determine whether the expressions are equivalent.
Part A:
Expressions: [tex]\(3z + 2z\)[/tex] and [tex]\(5z\)[/tex]
Step-by-Step:
- Combine like terms in the first expression: [tex]\(3z + 2z = 5z\)[/tex]
- The simplified form of both expressions is [tex]\(5z\)[/tex].
Since both expressions simplify to the same form:
- Answer: Yes
Part B:
Expressions: [tex]\((8x - 8x) - y\)[/tex] and [tex]\(0\)[/tex]
Step-by-Step:
- Simplify inside the parentheses: [tex]\(8x - 8x = 0\)[/tex]
- The expression simplifies to [tex]\(0 - y\)[/tex] which is [tex]\(-y\)[/tex]
- The second expression is [tex]\(0\)[/tex].
Since [tex]\(-y\)[/tex] is not equal to [tex]\(0\)[/tex]:
- Answer: No
Part C:
Expressions: [tex]\(9.1 + 4.5a - 2.5a\)[/tex] and [tex]\(11.1a\)[/tex]
Step-by-Step:
- Combine like terms in the first expression: [tex]\(4.5a - 2.5a = 2a\)[/tex]
- The first expression simplifies to [tex]\(9.1 + 2a\)[/tex]
- The second expression remains [tex]\(11.1a\)[/tex].
Since [tex]\(9.1 + 2a\)[/tex] is not equal to [tex]\(11.1a\)[/tex]:
- Answer: No
Part D:
Expressions: [tex]\(-7y \times 3 - 3\)[/tex] and [tex]\(0\)[/tex]
Step-by-Step:
- Perform the multiplication in the first expression: [tex]\(-7y \times 3 = -21y\)[/tex]
- The expression becomes [tex]\(-21y - 3\)[/tex]
- The second expression is [tex]\(0\)[/tex].
Since [tex]\(-21y - 3\)[/tex] is not equal to [tex]\(0\)[/tex]:
- Answer: No
Part E:
Expressions: [tex]\(y - 6 \times 3\)[/tex] and [tex]\(y - 18\)[/tex]
Step-by-Step:
- Perform the multiplication in the first expression: [tex]\(6 \times 3 = 18\)[/tex]
- The expression becomes [tex]\(y - 18\)[/tex]
- The second expression is [tex]\(y - 18\)[/tex].
Since both expressions simplify to the same form:
- Answer: Yes
Hence, the answers to the questions are:
- A: Yes
- B: No
- C: No
- D: No
- E: Yes
