3:11a And they sang responsively with praise and thanksgiving to the LORD:

They responded ⌊to what Yahweh had done⌋ by singing to praise and thank him:
-or-
⌊As they played the musical instruments,⌋ the people sang in praise of Yahweh and thanked him.

3:11b “For He is good; for His loving devotion to Israel endures forever.”

“Yahweh is good. His loyalty/faithfulness to Israel will never end/stop.”
-or-
⌊They sang:⌋ “Yahweh is good. He never stops showing/doing kindness to us, his people Israel, ⌊because he has made a covenant/agreement with us⌋.”

3:11c Then all the people gave a great shout of praise to the LORD,

And the congregation/assembly praised Yahweh with a great/loud shout
-or-
All the people responded by shouting out in praise to/of Yahweh.

3:11d because the foundation of the house of the LORD had been laid.

because the foundation of the house of Yahweh had been put in place.
-or-
They did this because ⌊they were so happy that⌋ the workmen had finished restoring/repairing the foundation of Yahweh’s temple.

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