To determine which choices can be used to verify the equation [tex]\( 205 - 110 = 95 \)[/tex], let's examine each choice step by step.
1. Check the equation [tex]\( 205 + 95 = 300 \)[/tex]:
For this equation to be true, we need to evaluate:
[tex]\[
205 + 95 = 300
\][/tex]
Simplifying the left-hand side:
[tex]\[
205 + 95 = 300
\][/tex]
This is incorrect because:
[tex]\[
205 + 95 = 300
\][/tex]
Hence, Choice 1 is incorrect.
2. Check the equation [tex]\( 110 + 95 = 205 \)[/tex]:
For this equation to be true, we need to evaluate:
[tex]\[
110 + 95 = 205
\][/tex]
Simplifying the left-hand side:
[tex]\[
110 + 95 = 205
\][/tex]
This is correct because:
[tex]\[
110 + 95 = 205
\][/tex]
Hence, Choice 2 is correct.
3. Check the equation [tex]\( 205 + 110 + 95 = 410 \)[/tex]:
For this equation to be true, we need to evaluate:
[tex]\[
205 + 110 + 95 = 410
\][/tex]
Simplifying the left-hand side:
[tex]\[
205 + 110 + 95 = 410
\][/tex]
This is incorrect because:
[tex]\[
205 + 110 + 95 = 410
\][/tex]
Hence, Choice 3 is incorrect.
4. Check the equation [tex]\( 205 + 110 = 315 \)[/tex]:
For this equation to be true, we need to evaluate:
[tex]\[
205 + 110 = 315
\][/tex]
Simplifying the left-hand side:
[tex]\[
205 + 110 = 315
\][/tex]
This is incorrect because:
[tex]\[
205 + 315 = 315
\][/tex]
Hence, Choice 4 is incorrect.
Summarizing, the only correct choice that can be used to verify the equation [tex]\( 205 - 110 = 95 \)[/tex] is:
- [tex]\( 110 + 95 = 205 \)[/tex]
Therefore, the correct choices are:
[tex]\[
(2, [1, 2, 3, 4])
\][/tex]
