Question

1) Quais das seguintes sentenças são inequações?
a) x-3 = 10
b) x + 4 <0
c) 5x 2 1 - 2x
e) ***2 = 4x
1) 2 + 3+1<7
i) - 422x - 6+x
d) x + y = 4
g) 7(x + 1) = 6 - 5x
1+3>-*
h) 3(x - 2) S 7x - 2​

Answer 1

a) x-3 = 10

$x-3=10\quad :\quad x=13\\\\x-3+3=10+3\\\\x=13$

b) x + 4 <0

$x+4<0\quad :\quad \begin{bmatrix}\mathrm{Solucao:}\:&\:x<-4\:\\ \:\mathrm{Notacao\:intervalo}&\:\left(-\infty \:,\:-4\right)\end{bmatrix}$

x+4-4<0-4

x<-4

Linha Numérica

c) 5x 2 1 - 2x

$5x\cdot \:21-2x=103x\\\\5x\cdot \:21-2x\\\\105x-2x\\\\103x$

e) ***2 = 4x

NÃO ENTEDIE

1) 2 + 3+1<7

$2+3+1<7\quad :\quad \begin{bmatrix}\mathrm{Solucao:}\:&\:\mathrm{Verdadeiro\:para\:todo\:}y_{789}\:\\ \:\mathrm{Notacao\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

2+3+1<7

2+3+1<7

verdadeiro

i) - 422x - 6+x

-422x-6+x=-421x-6

-422x-6+x

-422x+x-6

-421x-6

d) x + y = 4

$\mathrm{Forma\:inclinacao-intercepto\:de}\:x+y=4:\quad y=-x+4\\\\\mathrm{Dominio\:de\:}\:-x+4\::\quad \begin{bmatrix}\mathrm{Solucao:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Notacao\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Imagem\:de\:}-x+4:\quad \begin{bmatrix}\mathrm{Solucao:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Notacao\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Paridade\:de}\:-x+4:\quad \mathrm{Nao\:e\:par\:nem\:impar}$

$\mathrm{Pontos\:de\:interseccao\:com\:o\:eixo\:de}\:-x+4:\quad \mathrm{X\:intersepta}:\:\left(4,\:0\right),\:\mathrm{Y\:intersepta}:\:\left(0,\:4\right)\\\\\mathrm{Inversa\:de}\:-x+4:\quad 4-x\\\\\mathrm{Inclinacao\:de\:}-x+4:\quad m=-1$

g) 7(x + 1) = 6 - 5x  1+3>-*

$7\left(x+1\right)=6-5x\cdot \:1+3\quad :\quad x=\frac{1}{6}\quad \left(\mathrm{Decimal}:\quad x=0.16666\dots \right)\\\\\\7\left(x+1\right)=6-5x\cdot \:1+3\\\\7\left(x+1\right)=6-5x+3\\\\7\left(x+1\right)=-5x+6+3\\\\7\left(x+1\right)=-5x+9\\\\7x+7=-5x+9\\\\7x+7-7=-5x+9-7\\\\7x=-5x+2\\\\7x+5x=-5x+2+5x\\\\\\12x=2\\\\\frac{12x}{12}=\frac{2}{12}\\\\x=\frac{1}{6}$

h) 3(x - 2) S 7x - 2​

$3\left(x-2\right)S\cdot \:7x-2=21xS\left(x-2\right)-\\\\3\left(x-2\right)S\cdot \:7x-2\\\\21xS\left(x-2\right)-2$

A Linha Numérica da (B ) x + 4 <0