Question

Sa se afle x∈R pentru care diferenta expresiilor 2-x/3 si 7x+1/2 este mai mare decit 1
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Answer 1

$\dfrac{^{\big{2)}}2-x}{3} - \dfrac{^{\big{3)}}7x+1}{2} \ \textgreater \ ^{\big{6)}}1 \Rightarrow \dfrac{ 2(2-x)-3(7x+1)}{6} \ \textgreater \ \dfrac{6}{6} \Big|\cdot 6 \Rightarrow \\ \\ \Rightarrow 2(2-x)-3(7x+1) \ \textgreater \ 6 \Rightarrow 4-2x-21x-3 \ \textgreater \ 6 \Rightarrow \\ \\ \Rightarrow -23x\ \textgreater \ 6+3-4 \Rightarrow -23x \ \textgreater \ 5 \Big| \cdot(-1) \Rightarrow 23x\ \textless \ -5 \Rightarrow x \ \textless \ - \dfrac{5}{23} \Rightarrow \\ \\ \Rightarrow \boxed{x\in\Big(-\infty, - \dfrac{5}{23}\Big)}$

Answer 2

"Sa se afle x∈R pentru care diferenta expresiilor 2-x/3 si 7x+1/2 este mai mare decit 1"

Să se afle x∈ℝ, pentru care diferența expresiilor (2 - x)/3  și (7x+1)/2  

este  mai mare decât 1.

R:

[tex]\it \dfrac{^{2)}2-x}{3} -\dfrac{^{3)} 7x+1}{2} \ \textgreater \ \ ^{6)}1 \Leftrightarrow 4-2x-21x-3\ \textgreater \ 6 \Leftrightarrow 1-23x\ \textgreater \ 6 \\\;\\ \\\;\\ \Leftrightarrow 1-6\ \textgreater \ 23x \Leftrightarrow-5\ \textgreater \ 23x \Leftrightarrow23x\ \textless \ -5 \Leftrightarrow x\ \textless \ -\dfrac{5}{23} \\\;\\ \\\;\\ S = (-\infty,\ \ -\dfrac{5}{23})[/tex]