Question

O menor numero inteiro que satisfaz a inequaçao 3+5x/6 <1/4 +x

Answer 1

Resolução:

$\mathsf{3+\dfrac{5x}{6}\ \textless \ \dfrac{1}{4}+x}\\\\\\\mathsf{\dfrac{5x}{6}-x\ \textless \ \dfrac{1}{4}-3}\\\\\\\mathsf{\dfrac{5x}{6}-\dfrac{6\cdot x}{6}\ \textless \ \dfrac{1}{4}-\dfrac{4\cdot 3}{4}}\\\\\\\mathsf{\dfrac{5x-6x}{6}\ \textless \ \dfrac{1-12}{4}}\\\\\\\mathsf{\dfrac{5x-6x}{3}\ \textless \ \dfrac{1-12}{2}}\\\\\\\mathsf{-\dfrac{x}{3}\ \textless \ -\dfrac{11}{2}}$

Multiplicando ambos os lados por -1, invertendo o sinal da desigualdade:

$\mathsf{\dfrac{x}{3}\ \textgreater \ \dfrac{11}{2}}\\\\\\\mathsf{x\ \textgreater \ \dfrac{11\cdot 3}{2}}\\\\\\\mathsf{x\ \textgreater \ \dfrac{33}{2}}\\\\\\\mathsf{x\ \textgreater \ 16,5}$

O conjunto dos números inteiros é determinado por:

$\boxed{\mathsf{\left(...,-3,-2,-1,0,1,2,3,...\right)}}$

No qual o valor de $\mathsf{x}$ deve ser maior que 16,5. Logo o menor valor inteiro que $\mathsf{x}$ pode assumir é o 17.

= = = = =

$\boxed{\mathsf{Resposta:\:O\:menor\:n\'{u}mero\:inteiro\:que\:satisfaz\:a\:inequac\~{a}o\:\'{e}\:o\:17}}\: \: \checkmark$