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The phrase "inability to solve" is correct and usable in written English.
You can use it when you are referring to someone's inability to solve a problem or come up with a solution. For example, "His inability to solve the puzzle was frustrating."
Exact(54)
We look at Carson's pain, her inability to solve her problems.
Ma is bitter about Erik's inability to solve our practical problems.
Symptoms can include forgetfulness, confusion, and the new inability to solve routine problems.
President Obama's inability to solve the nation's economic woes has only reinforced the right's ideological advantage.
The 1,357-page 1,357-pagegely ascreportthe authorities' inabilargely solve the cascribedbiases harbored by individual officers.
In practice, this new pluralistic world has given rise to globosclerosis, an inability to solve problem after problem.
Similar(6)
It's a suit of armour against their own inability to actually solve anything.
The escalating crisis of confidence around the world is a phenomenon linked not only the global financial crisis but also to the uncertainty surrounding many governments — from the Middle East's transitional democracies and Europe's debt-strapped countries to the U.S.'s inability to collaboratively solve its own serious problems.
Historically, the Study effect has been considered a fixed effect not because of a strong argument that such effect is indeed fixed but because of our prior inability to efficiently solve even modest-sized mixed models (those containing both fixed and random effects).
Typical challenges identified by families recovering from TBI include: frustration and impatience with one another, loss of former lives and relationships, difficulty setting reasonable goals, inability to effectively solve problems as a family, increased level of stress and household tension, changes in emotional dynamics, and overwhelming desire to return to pre-injury status.
What is most perplexing is the seeming inability of executives to solve — and satisfactorily explain — the manufacturing issues that dog the company.
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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