1. Identify the total number of amino acid residues

The peptide gives on complete hydrolysis:

• $3$ moles of glycine
• $2$ moles of leucine
• $2$ moles of valine

So, total amino acid units in one molecule of peptide are: $3+2+2=7$

Thus, the peptide contains 7 amino acid residues.

2. Relation between amino acids and peptide linkages

If a peptide contains $n$ amino acid residues in a single chain, then the number of peptide bonds (linkages) is: $n-1$

Here, $n=7$, so $7-1=6$

3. Final answer

The number of peptide linkages is: $\boxed{6}$

4. Comparison with stored correct answer

Stored correct answer = $6$

Our derived answer = $6$

Hence, the answer agrees with the stored correct answer.