Question

solution set for 2(x - 1)/5 < or = 3(2 + x)/7​

Answer 1

Answer:

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Answer 2

$Given \: inequality :\\\frac{ 2(x-1)}{5} \leq \frac{3(2+x)}{7}$

Finding LCM of 5 and 7 :

$L.C.M ( 5,7) = 5 \times 7 = 35$

/* Multiplying bothsides of inequality by 35, we get */

$\implies \frac{ 35 \times 2(x-1)}{5} \leq \frac{35 \times 3(2+x)}{7}$

$\implies 7\times 2(x-1) \leq 5 \times 3(2+x)$

$\implies 14(x-1) \leq 15(2+x)$

$\implies 14x - 14 \leq 30 + 15x$

/* Subtract bothsides of the inequality by 14x , we get */

$\implies 14x - 14 - 14x \leq 30 + 15x - 14x$

$\implies - 14 \leq 30 + x$

/* Subtract bothsides of the inequality by 30 , we get */

$\implies - 14 - 30 \leq 30 + x - 30$

$\implies - 44 \leq x$

$\implies x \geq -44$

Therefore.,

$\green{ Value \: of \: x \geq -44 }$

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