Let's simplify the expression step by step:
Given expression:
[tex]\[ 3j - \{2k - [5h - (3j + k)]\} \][/tex]
First, resolve the innermost brackets:
[tex]\[ 5h - (3j + k) \][/tex]
This simplifies to:
[tex]\[ 5h - 3j - k \][/tex]
Now, substitute this result back into the expression within the second set of brackets:
[tex]\[ 3j - \{2k - (5h - 3j - k)\} \][/tex]
Next, distribute the negative sign in front of the parentheses:
[tex]\[ 2k - 5h + 3j + k \][/tex]
Combine like terms inside the braces:
[tex]\[ 2k + k + 3j - 5h = 3k + 3j - 5h \][/tex]
Now, substitute this result back into the original expression:
[tex]\[ 3j - (3k + 3j - 5h) \][/tex]
Distribute the negative sign in front of the parentheses:
[tex]\[ 3j - 3k - 3j + 5h \][/tex]
Combine like terms:
[tex]\[ 5h - 3k \][/tex]
Thus, the simplified expression is:
[tex]\[ 5h - 3k \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{5h - 3k} \][/tex]
