To solve the problem of creating two expressions using the given numbers [tex]\(-4, 10, 8, 2, -3, -5\)[/tex] that equal 6, let's walk through the solution step-by-step.
### Expression 1:
1. Identify numbers that can sum or differ to equal 6:
- We can identify that [tex]\(10\)[/tex] and [tex]\(-4\)[/tex] have a straightforward relationship.
2. Form the expression:
- By subtracting [tex]\(-4\)[/tex] from [tex]\(10\)[/tex], we get:
[tex]\[
10 + (-4) = 10 - 4 = 6
\][/tex]
So, one valid expression is:
[tex]\[ 10 + (-4) = 6 \][/tex]
### Expression 2:
1. Identify another set of numbers:
- We need to find another combination. Let's consider [tex]\(8\)[/tex], [tex]\(2\)[/tex], and [tex]\(-4\)[/tex].
2. Form the expression:
- We can add [tex]\(8\)[/tex] and [tex]\(2\)[/tex], and then subtract [tex]\(-4\)[/tex]:
[tex]\[
8 + 2 + (-4) = 8 + 2 - 4
\][/tex]
- Simplifying within the parentheses, we get:
[tex]\[
8 + 2 - 4 = 10 - 4 = 6
\][/tex]
So, another valid expression is:
[tex]\[ 8 + 2 + (-4) = 6 \][/tex]
### Summary:
To sum up, the two expressions that equal 6 by using the provided numbers are:
1. [tex]\(10 + (-4) = 6\)[/tex]
2. [tex]\(8 + 2 + (-4) = 6\)[/tex]
Both expressions correctly result in the number 6.
