Question

Помогите по алгебре решить​

Answer 1

Ответ:

$1)\ \ \left\{\begin{array}{l}2x+3>7\\x-5\geq 1\end{array}\right\ \ \left\{\begin{array}{l}2x>4\\x\geq 6\end{array}\right\ \ \left\{\begin{array}{l}x>2\\x\geq 6\end{array}\right\ \ \ \ \ \ x\in [\ 6\ ;+\infty \, )$

$2)\ \ \left\{\begin{array}{l}3(x+8)\geq 4(7-x)\\(x+2)(x-5)\geq (x+3)(x-4)\end{array}\right\ \ \left\{\begin{array}{l}3x+24\geq 28-4x\\x^2-3x-10\geq x^2-x-12\end{array}\right\\\\\\\left\{\begin{array}{l}7x\geq 4\\-2x\geq -2\end{array}\right\ \ \left\{\begin{array}{l}x\geq \dfrac{4}{7}\\x\leq 1\end{array}\right\ \ \ \ x\in \Big[\ \dfrac{4}{7} \ ;\ 1\ \Big]$

$3)\ \ \left\{\begin{array}{l}3-\dfrac{x-2}{2}<x\\5(x-2)<8x+1\end{array}\right\ \ \left\{\begin{array}{l}6-x+2<2x\\5x-10<8x+1\end{array}\right\ \ \left\{\begin{array}{l}3x>8\\3x>-11\end{array}\right\\\\\\\left\{\begin{array}{l}x>2\dfrac{2}{3}\\x>-3\dfrac{2}{3}\end{array}\right\ \ \ \ \ \ \ x\in \Big(2\dfrac{2}{3}\ ;+\infty \, \Big)$