Question

resolva as seguintes inequações ir: a)2x+1≤x+6 b)2-3≥x+14 c)2(x+3)>3(1-x)

Answer 1

a) 2x + 1 ≤ x + 6
2x - x ≤ 6 - 1
x ≤ 5

b)2 - 3 ≥ x + 14
-x ≥ 14 - 2 + 3
-x ≥ 15 (ao multiplicar por -1 , vc troca também o lado do < e >)
x ≤ -15

c)2 (x + 3) > 3 (1 - x)
2x + 6 > 3 - 3x
2x + 3x > 3 - 6
5x > -3
x > -3/5

Answer 2

Resposta:

$a)\:S=\{x\in\mathbb{R}/x\leq 5\}$

$b)\:S=\{x\in\mathbb{R}/x\leq-15 \}$

$c)\:S=\{x\in\mathbb{R}/x>-\frac{3}{5} \}$

Explicação passo-a-passo:

$a)\:2x+1\leq x+6\\2x-x\leq 6-1\\\boxed{x\leq 5}$

$b)\:2-3\geq x+14\\-1\geq x+14\\-x\geq 14+1\\-x\geq 15\:\times(-1)\\\boxed{x\leq -15}$

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