To determine which integer added to [tex]\(-4\)[/tex] yields [tex]\(5\)[/tex], let's break this down step-by-step:
1. Problem Setup: We are given the equation [tex]\[ x + (-4) = 5. \][/tex]
2. Isolate [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], we need to move [tex]\(-4\)[/tex] to the other side of the equation. This can be done by adding [tex]\(4\)[/tex] to both sides:
[tex]\[ x + (-4) + 4 = 5 + 4. \][/tex]
3. Simplification: By performing the addition on both sides, we simplify:
[tex]\[ x = 9. \][/tex]
4. Verification: To ensure that our solution is correct, we should verify by substituting [tex]\(x = 9\)[/tex] back into the original equation:
[tex]\[ 9 + (-4) = 5. \][/tex]
However, let's verify this:
[tex]\[ 9 + (-4) = 9 - 4 = 5. \][/tex]
The left-hand side equals [tex]\(5\)[/tex] after simplification, confirming the equation is properly balanced and our solution is correct.
Thus, the integer that, when added to [tex]\(-4\)[/tex], gives [tex]\(5\)[/tex] is [tex]\(\boxed{9}\)[/tex].
