High School

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For the expression in each row, select an equivalent expression in one of the columns.

[tex]
\[
\begin{array}{ll}
94 - 21 & \\
21 - (-94) & 94 + 21 \\
94 + (-21) & 0 \\
\end{array}
\]
[/tex]

Answer :

Sure! Let's go through the question step-by-step to find the equivalent expressions:

1. Expression Analysis:

- First Row Expression:
- [tex]\( 94 - 21 \)[/tex]

- Second Row Expressions:
- [tex]\( 21 - (-94) \)[/tex]
- [tex]\( 94 + 21 \)[/tex]

- Third Row Expression:
- [tex]\( 94 + (-21) \)[/tex]
- 0 (Zero)

2. Calculate and Compare:

- For the expression [tex]\( 94 - 21 \)[/tex]:
- Calculate [tex]\( 94 - 21 \)[/tex]. The result is 73.

- Find equivalent expressions:

a. Checking [tex]\( 94 + (-21) \)[/tex]:
- Simplifying [tex]\( 94 + (-21) \)[/tex] gives [tex]\( 94 - 21 \)[/tex], which is 73.
- Therefore, [tex]\( 94 - 21 \)[/tex] is equivalent to [tex]\( 94 + (-21) \)[/tex].

b. Checking other expressions:
- [tex]\( 21 - (-94) \)[/tex] is the same as [tex]\( 21 + 94 \)[/tex], which is not 73.
- [tex]\( 94 + 21 \)[/tex] results in a different value and is not the same as 73.
- 0 is not equivalent to 73.

- For the expression [tex]\( 21 - (-94) \)[/tex]:
- Simplify [tex]\( 21 - (-94) \)[/tex] to [tex]\( 21 + 94 \)[/tex], which equals 115.

- Finding equivalent expressions:

a. Checking [tex]\( 94 + 21 \)[/tex]:
- Calculate [tex]\( 94 + 21 \)[/tex], which is 115.
- Thus, [tex]\( 21 - (-94) \)[/tex] is equivalent to [tex]\( 94 + 21 \)[/tex].

b. Checking other expressions:
- [tex]\( 94 - 21 \)[/tex] is not 115.
- [tex]\( 94 + (-21) \)[/tex] gives a different value, which is 73.
- 0 is not equivalent to 115.

3. Conclusion:
- [tex]\( 94 - 21 \)[/tex] is equivalent to [tex]\( 94 + (-21) \)[/tex].
- [tex]\( 21 - (-94) \)[/tex] is equivalent to [tex]\( 94 + 21 \)[/tex].

I hope this step-by-step explanation helps you understand how these expressions are equivalent!

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