Question

A) 6×=2× +16
B)2× -5= ×+1
C)2× +3=× +4
D)5× +7=4× +10
E)4× -10=2× +2
F)4× -7=8× -2
G)2× +1=4× -7
H)9× +9 +3×=15
I)16× -1=12×+3
J)3× -2=4×+9
K)5× -3+×=2×+9
L)17×-7×=×+18
M)×+×-4=17-2×+1
N)×+2×+3-5×=4×-9
O)5×+6×-16=3×+2×-4
P)5×+4=3×-2×+4
Q) 3x-4=2x+8
R)7x-2+4=10+5x
S)
2x+4=-x
T)4x+10=2x-2

Answer 1

Resposta:

Explicação passo-a-passo:

a)

6x=2x+16 => 6x-2x=16 => 4x=16 => x=16/4 =>x=4

b)

2x-5=x+1 =>  2x-x=1+5 => x=6

c)

2x+3=x+4 => 2x-x=4-3 => x=1

d)

5x+7=4x+10 => 5x-4x=10-7 => x=3

e)

4x-10=2x+2 => 4x-2x=2+10 => 2x=12 => x=12/2 => x=6

f)

4x-7=8x-2 => 8x-4x=2-7 => 4x= -5 => x= -5/4

g)

2x+1=4x-7 => 4x-2x=1+7 => 2x=8 => x=8/2 => x=4

h)

9x+9+3x=15 => 12x=15-9 => 12x=6 => x=6÷6/12÷6 => x=1/2

i)

16x-1=12x+3 => 16x-12x=3+1 => 4x=4 => x=4/4 => x=1

j)

3x-2=4x+9 => 4x-3x= -2-9 => x= -11

k)

5x-3+x=2x+9 => 5x-2x+x=9+3 => 4x=12 => x=12/4 => x=3

l)

17x-7x=x+18 => 10x-x=18 => 9x=18 => x=18/9 => x=2

m)

x+x-4=17-2x+1 => 2x+2x=18+4 => 4x=22 => x=22/4 => x=11/2

n)

x+2x+3-5x=4x-9 => -2x+3=4x-9 => 4x+2x=3+9 => 6x=12 => x=12/6 => x=2

o)

5x+6x-16=3x+2x-4 => 11x-16=5x-4 => 11x-5x=16-4 => 6x=12 => x=12/6 => x=2

p)

5x+4=3x-2x+4 => 5x+4=x+4 => 5x-x=4-4 => 4x=0 => x=0/4 => x=0

q)

3x-4=2x+8 => 3x-2x=8+4 => x=12

r)

7x-2+4=10+5x => 7x-5x+4=10 => 2x=10-4 => 2x=6 => x=6/2 => x=3

s)

2x+4=-x => 2x+x= -4 => 3x= -4 => x= -4/3

t)

4x+10=2x-2 => 4x-2x= -10-2 => 2x= -12 => x= -12/2 => x= -6

Answer 2

Para resolver estas equações do 1º grau, a ideia é isolar x dos números para encontrar o seu valor que satisfaz a igualdade.

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Letra A

$\begin{array}{l}\sf6x=2x+16\\\\\sf-2x+6x=2x+16-2x\\\\\sf4x=16\\\\\sf\dfrac{4x}{4}=\dfrac{16}{4}\\\\\!\boxed{\sf x=4}\end{array}$

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Letra B

$\begin{array}{l}\sf2x-5=x+1\\\\\sf-x+2x-5=x+1-x\\\\\sf x-5=1\\\\\sf5+x-5=1+5\\\\\!\boxed{\sf x=6}\end{array}$

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Letra C

$\begin{array}{l}\sf2x+3=x+4\\\\\sf-x+2x+3=x+4-x\\\\\sf x+3=4\\\\\sf -3+x+3=4-3\\\\\!\boxed{\sf x=1}\end{array}$

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Letra D

$\begin{array}{l}\sf5x+7=4x+10\\\\\sf-4x+5x+7=4x+10-4x\\\\\sf x+7=10\\\\\sf -7+x+7=10-7\\\\\!\boxed{\sf x=3}\end{array}$

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Letra E

$\begin{array}{l}\sf4x-10=2x+2\\\\\sf-2x+4x-10=2x+2-2x\\\\\sf2x-10=2\\\\\sf 10+2x-10=2+10\\\\\sf2x=12\\\\\sf\dfrac{2x}{2}=\dfrac{12}{2}\\\\\!\boxed{\sf x=6}\end{array}$

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Letra F

$\begin{array}{l}\sf4x-7=8x-2\\\\\sf-8x+4x-7=8x-2-8x\\\\\sf-4x-7=-2\\\\\sf 7-4x-7=-2+7\\\\\sf(-4x=5)\cdot(-1)\\\\\sf4x=-5\\\\\sf\dfrac{4x}{4}=-\dfrac{5}{4}\\\\\!\boxed{\sf x=-\dfrac{5}{4}}\end{array}$

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Letra G

$\begin{array}{l}\sf2x+1=4x-7\\\\\sf-4x+2x+1=4x-7-4x\\\\\sf-2x+1=-7\\\\\sf -1-2x+1=-7-1\\\\\sf(-2x=-8)\cdot(-1)\\\\\sf2x=8\\\\\sf\dfrac{2x}{2}=\dfrac{8}{2}\\\\\!\boxed{\sf x=4}\end{array}$

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Letra H

$\begin{array}{l}\sf9x+9+3x=15\\\\\sf12x+9=15\\\\\sf-9+12x+9=15-9\\\\\sf12x=6\\\\\sf\dfrac{12x}{12}=\dfrac{6}{12}\\\\\!\boxed{\sf x=\dfrac{1}{2}}\end{array}$

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Letra I

$\begin{array}{l}\sf16x-1=12x+3\\\\\sf-12x+16x-1=12x+3-12x\\\\\sf4x-1=3\\\\\sf1+4x-1=3+1\\\\\sf4x=4\\\\\sf\dfrac{4x}{4}=\dfrac{4}{4}\\\\\!\boxed{\sf x=1}\end{array}$

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Letra J

$\begin{array}{l}\sf3x-2=4x+9\\\\\sf-4x+3x-2=4x+9-4x\\\\\sf-x-2=9\\\\\sf2-x-2=9+2\\\\\sf(-x=11)\cdot(-1)\\\\\!\boxed{\sf x=-11}\end{array}$

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Letra K

$\begin{array}{l}\sf5x-3+x=2x+9\\\\\sf6x-3=2x+9\\\\\sf-2x+6x-3=2x+9-2x\\\\\sf4x-3=9\\\\\sf3+4x-3=9+3\\\\\sf4x=12\\\\\sf\dfrac{4x}{4}=\dfrac{12}{4}\\\\\!\boxed{\sf x=3}\end{array}$

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Letra L

$\begin{array}{l}\sf17x-7x=x+18\\\\\sf10x=x+18\\\\\sf-x+10x=x+18-x\\\\\sf9x=18\\\\\sf\dfrac{9x}{9}=\dfrac{18}{9}\\\\\!\boxed{\sf x=2}\end{array}$

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Letra M

$\begin{array}{l}\sf x+x-4=17-2x+1\\\\\sf2x-4=18-2x\\\\\sf2x+2x-4=18-2x+2x\\\\\sf4x-4=18\\\\\sf4+4x-4=18+4\\\\\sf4x=22\\\\\sf\dfrac{4x}{4}=\dfrac{22}{4}\\\\\!\boxed{\sf x=\dfrac{11}{2}}\end{array}$

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Letra N

$\begin{array}{l}\sf x+2x+3-5x=4x-9\\\\\sf-2x+3=4x-9\\\\\sf-4x-2x+3=4x-9-4x\\\\\sf-6x+3=-9\\\\\sf-3-6x+3=-9-3\\\\\sf(-6x=-12)\cdot(-1)\\\\\sf6x=12\\\\\sf\dfrac{6x}{6}=\dfrac{12}{6}\\\\\!\boxed{\sf x=2}\end{array}$

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Letra O

$\begin{array}{l}\sf5x+6x-16=3x+2x-4\\\\\sf11x-16=5x-4\\\\\sf-5x+11x-16=5x-4-5x\\\\\sf6x-16=-4\\\\\sf16+6x-16=-4+16\\\\\sf6x=12\\\\\sf\dfrac{6x}{6}=\dfrac{12}{6}\\\\\!\boxed{\sf x=2}\end{array}$

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Letra P

$\begin{array}{l}\sf5x+4=3x-2x+4\\\\\sf5x+4=x+4\\\\\sf-x+5x+4=x+4-x\\\\\sf4x+4=4\\\\\sf-4+4x+4=4-4\\\\\sf4x=0\\\\\sf\dfrac{4x}{4}=\dfrac{0}{4}\\\\\!\boxed{\sf x=0}\end{array}$

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Letra Q

$\begin{array}{l}\sf3x-4=2x+8\\\\\sf-2x+3x-4=2x+8-2x\\\\\sf x-4=8\\\\\sf4+x-4=8+4\\\\\!\boxed{\sf x=12}\end{array}$

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Letra R

$\begin{array}{l}\sf7x-2+4=10+5x\\\\\sf7x+2=10+5x\\\\\sf-5x+7x+2=10+5x-5x\\\\\sf2x+2=10\\\\\sf-2+2x+2=10-2\\\\\sf2x=8\\\\\sf\dfrac{2x}{2}=\dfrac{8}{2}\\\\\!\boxed{\sf x=4}\end{array}$

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Letra S

$\begin{array}{l}\sf2x+4=-x\\\\\sf x+2x+4=-x+x\\\\\sf3x+4=0\\\\\sf-4+3x+4=0-4\\\\\sf3x=-4\\\\\sf\dfrac{3x}{3}=-\dfrac{4}{3}\\\\\!\boxed{\sf x=-\dfrac{4}{3}}\end{array}$

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Letra T

$\begin{array}{l}\sf4x+10=2x-2\\\\\sf-2x+4x+10=2x-2-2x\\\\\sf2x+10=-2\\\\\sf-10+2x=-2-10\\\\\sf2x=-12\\\\\sf\dfrac{2x}{2}=-\dfrac{12}{2}\\\\\!\boxed{\sf x=-6}\end{array}$

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Att. Nasgovaskov