Question

resolva as seguintes inequações ,em R :

A)
$2x + 1 \leqslant x + 6$
B)
$2 - 3x \geqslant x + 14$
C)
$2(x + 3) > 3(1 - x)$
D)
$3(1 - 2x) < 2(x + 1) + x - 7$


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Answer 1

Resposta:

Explicação passo-a-passo:

I. 2x + 1 ≤ x + 6

$2x + 1 \leq x + 6\\2x-x\leq 6-1\\x\leq 5$

S = { x ∈ R | x ≤ 5 }

II. 2 - 3x ≥ x + 14

$2 - 3x \geq x + 14\\-3x-x\geq 14-2\\-4x\geq 12\\-x\geq 3\:\:\:\:.(-1)\\x\leq -3$

S = { x ∈ R | x ≤ -3 }

III. 2 ( x + 3 ) > 3 ( 1 - x )

$2 ( x + 3 ) > 3 ( 1 - x )\\2x+6>3-3x\\2x+3x>3-6\\5x>-3\\x>-\frac{3}{5}$

S = { x ∈ R | x > -3/5 }

IV. 3 ( 1 - 2x ) < 2 ( x + 1 ) + x - 7

$3 ( 1 - 2x ) < 2 ( x + 1 ) + x - 7\\3-6x<2x+2+x-7\\-6x-2x-x<-7+2-3\\-9x<-8\:\:\:\:\:.(-1)\\x > \frac{8}{9}$

S = { x ∈ R | x > 8/9 }

Espero ter ajudado!

Desculpe qualquer erro.