To determine which of the given expressions is equal to [tex]\( 6 + (2 + 3) \times 5 \)[/tex], let's evaluate each step-by-step.
First, simplify the given expression [tex]\( 6 + (2 + 3) \times 5 \)[/tex]:
1. Evaluate the parentheses:
[tex]\[
2 + 3 = 5
\][/tex]
2. Substitute back into the expression:
[tex]\[
6 + 5 \times 5
\][/tex]
3. Evaluate the multiplication:
[tex]\[
5 \times 5 = 25
\][/tex]
4. Add the results:
[tex]\[
6 + 25 = 31
\][/tex]
So, the given expression simplifies to 31.
Now, let’s compare this result to each of the given expressions:
1. [tex]\( 1 + 10 \times 3 \)[/tex]
- Evaluate the multiplication:
[tex]\[
10 \times 3 = 30
\][/tex]
- Add the result to 1:
[tex]\[
1 + 30 = 31
\][/tex]
This expression simplifies to 31, which matches the given expression.
2. [tex]\( (4 \times 5) + 3 \)[/tex]
- Evaluate the multiplication:
[tex]\[
4 \times 5 = 20
\][/tex]
- Add the result to 3:
[tex]\[
20 + 3 = 23
\][/tex]
This expression simplifies to 23, which does not match the given expression.
3. [tex]\( 9 \times 5 + 10 \)[/tex]
- Evaluate the multiplication:
[tex]\[
9 \times 5 = 45
\][/tex]
- Add the result to 10:
[tex]\[
45 + 10 = 55
\][/tex]
This expression simplifies to 55, which does not match the given expression.
4. [tex]\( 5 + 4 \times (5 - 6) \)[/tex]
- Evaluate the parentheses:
[tex]\[
5 - 6 = -1
\][/tex]
- Evaluate the multiplication:
[tex]\[
4 \times (-1) = -4
\][/tex]
- Add the result to 5:
[tex]\[
5 + (-4) = 1
\][/tex]
This expression simplifies to 1, which does not match the given expression.
The expression that equals [tex]\( 6 + (2 + 3) \times 5 \)[/tex], which is 31, is [tex]\( 1 + 10 \times 3 \)[/tex].
Hence, the correct expression is:
[tex]\[
1 + 10 \times 3
\][/tex]
So, the answer is:
[tex]\[
\boxed{1}
\][/tex]
