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Discover LudwigThe phrase "backing of the" is correct and can be used in written English.
It is commonly used to describe support or approval from someone or a group of people. Example: The mayor's proposal received the backing of the city council, ensuring its approval.
Idiom
Back-of-the-envelope calculation.
A back of the envelope calculation is a figure that was arrived at quickly or by using estimation--as if someone had grabbed the first scrap of paper they found and made a quick guess.
Exact(60)
He claimed the backing of the Institute for Fiscal Studies.
They need the backing of the league.
They have the backing of the Defence Secretary, Philip Hammond.
The backing of the West gives Saudi's position legitimacy.
And they have the backing of the government.
The commissions have the backing of the international community.
The unions have the backing of the far left.
The protest had the backing of the Mexico City government.
Besides, it has the backing of the United States.
The backing of the federation has U.S. players cautiously optimistic.
Shields has the backing of the Liverpool team.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com