Solve the inequality $$ 35^x+20^x+15^x\le28^x+21^x+25^x, $$ for $x\in\mathbb{R}$.
I tried to find the solution by hand and to prove that they are the only ones. I saw that $x=0$ verifies the inequality. But now, I don't know what is the next step.
2026-04-02 03:12:08.1775099528
Using analysis in solving exponential inequalities
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It's $$(7^x-5^x)(4^x+3^x-5^x)\geq0.$$ Can you end it now?
I got $0\leq x\leq2.$