Question

•Resolva os seguintes sistemas de inequações:

A)
$2x - 1 \geqslant 5$
$- x - 3 < 0$

B)
$x + 4 \leqslant 2x - 1$
$x + 1 \geqslant 0$
C)
$- 1 < 2x - 3 \leqslant x$
D)
$-2x \leqslant 3x + 7 < 4x$
me ajudem pleaseee!!!!​

Answer 1

Explicação passo-a-passo:

a)

• $\sf 2x-1\ge5$

$\sf 2x\ge5+1$

$\sf 2x\ge6$

$\sf x\ge\dfrac{6}{2}$

$\sf x\ge3$

• $\sf -x-3 < 0$

$\sf -x < 3$

$\sf -x < 3~~~\cdot(-1)$

$\sf x>3$

Logo:

$\sf S=\{x\in\mathbb{R}~|~x>3\}$

b)

• $\sf x+4\le2x-1$

$\sf x-2x\le-1-4$

$\sf -x\le-5~~~\cdot(-1)$

$\sf x\ge5$

• $\sf x+1\ge0$

$\sf x\ge-1$

Logo:

$\sf S=\{x\in\mathbb{R}~|~x\ge5\}$

c)

$\sf -1 < 2x-3\le x$

• $\sf 2x-3>-1$

$\sf 2x>-1+3$

$\sf 2x>2$

$\sf x>\dfrac{2}{2}$

$\sf x>1$

• $\sf 2x-3\le x$

$\sf 2x-x\le3$

$\sf x\le3$

Logo:

$\sf S=\{x\in\mathbb{R}~|~1 < x\le3\}$

d)

$\sf -2x\le 3x+7 < 4x$

• $\sf 3x+7\ge-2x$

$\sf 3x+2x\ge-7$

$\sf 5x\ge-7$

$\sf x\ge\dfrac{-7}{5}$

• $\sf 3x+7 < 4x$

$\sf 3x-4x < -7$

$\sf -x < -7~~\cdot(-1)$

$\sf x>7$

Logo:

$\sf S=\{x\in\mathbb{R}~|~x>7\}$