Question

Answer 1

\(\dfrac{x+6}{5}-\dfrac{x-2}{3}< 2\)

<=> \(\dfrac{3\left(x+6\right)}{15}-\dfrac{5\left(x-2\right)}{15}< \dfrac{30}{15}\)

<=> 3(x + 6) - 5(x - 2) < 30

<=> 3x + 18 - 5x + 10 < 30

<=> 3x - 5x < 30 - 18 - 10

<=> -2x < 2

<=> -2x : (-2) < 2 : (-2)

<=> x > -1

Vậy nghiệm của BPT là \(S=\left\{x|x>-1\right\}\)

Answer 2

3(x+6)15−5(x−2)15<30153(x+6)15−5(x−2)15<3015

<=> 3(x + 6) - 5(x - 2) < 30

<=> 3x + 18 - 5x + 10 < 30

<=> 3x - 5x < 30 - 18 - 10

<=> -2x < 2

<=> -2x : (-2) < 2 : (-2)