Question

Vamos determinar a soluçao de cada uma das seguintes inequaçoes do 1°grau com uma incognita no conjunto dos numeros relativos (Q):a-x+21>30b-2x-1 > ou igual a 6.

c-1x>7x+10

d-2x+25 =/ 21-3x

e-17-x>23

f-7x+1<10x

g-13x+1>3x+21

h-9x-8>11x-10

i-3x-2+4x+12>x

j-8x-20>15x-9-32

l-9-3x+3-8+6x<0

Answer 1

a)
$x+21>30 \\ x>30-21 \\ x>9$

S={ x ∈ R / x > 9 }
b)
$2x-1 \geq 6 \\ 2x \geq 6+1 \\ 2x \geq 7$

$x \geq \frac{7}{2}$

S={ x ∈ R / x ≥ 7/2}

c)
$x>7x+10 \\ x-7x>10 \\ -6x>10 \\ 6x<-10$

$x<- \frac{10}{6} =- \frac{5}{3}$

S= { x ∈ R / x < $- \frac{5}{3}$ }

d)
$2x+25 \leq 21-3x \\ 2x+3x \leq 21-25 \\ 5x \leq -4$

$x \leq - \frac{4}{5}$

S={ x ∈ R / x ≤ $- \frac{4}{5}$ }

e)
$17-x>23 \\ -x>23-17 \\ -x>6 \\ x<-6$

S-{ x ∈ R / x < -6 }

f)
$7x+1<10x \\ 7x-10x<-1 \\ -3x<-1 \\ 3x>1$

$x> \frac{1}{3}$

S={ x ∈ R / x > 1/3 }

g)
$13x +1>3x+21 \\ 13x-3x>21-1 \\ 10x>20 \\ x>20\div10 \\ x>2$

S { x ∈ R / x > 2 }

h)
$9x-8>11x-10 \\ 9x-11x>-10+8 \\ -2x>-2 \\ 2x<2 \\ x<2\div2 \\ x<1$

S={ x ∈ R / x < 1 }

i)
$3x-2+4x+12>x \\ 3x+4x-x>-12+2 \\ 6x>-10$

$x>- \frac{10}{6} =- \frac{5}{3}$

S={ x ∈ R / x > -5/3 }

j)
$8x-20>15x-9-32 \\ 8x-15x>-9-32+20 \\ -7x>-41+20 \\ -7x>-21 \\ 7x<21 \\ x<21\div7 \\ x<3$

S={x ∈ R / x < 3 }

l)
$9-3x+3-8+6x<0 \\ -3x+6x<-9-3+8 \\ 3x<-12+8 \\ 3x<-4$

$x<- \frac{4}{3}$

S={ x ∈ R / x < -4/3 }