contestada

Simplify each equation and identify if it has no solution, one solution, or infinitely many solutions.
An equation that is always true has infinitely many solutions.

A. 6(x+2)-10=6x+2
B. 6(x+2)-12=6x+2
C. 6(x+2)-10=2x+10
D. 4x-2=4(x-2)+6
E. 2(3x-6)=6(-2+x)

Respuesta :

BigusBrainus

Answer:

[tex]a. \: 6x + 12 - 10 = 6x + 2 \\ 6x + 2 = 6x + 2 \\ infinite \: solutions \\ \\ b. \: 6x + 12 - 12 = 6x + 2 \\ 6x = 6x + 2 \\ no \: solutions \\ \\ c. \: 6x + 12 - 10 = 2x + 10 \\ 6x + 2 = 2x + 10 \\ 4x = 8 \\ x = 2 \\ one \: solution \\ \\ d. \: 4x - 2 = 4x - 8 + 6 \\ 4x - 2 = 4x - 2 \\ infinite \: solutions \\ e. \: 6x - 12 = - 12 + 6x \\ infinite \: solutions[/tex]

27spidersmart

Answer:

A) Infinitely Many Solutions

B) No Solution

C) One Solution (x = 2)

D) Infinitely Many Solutions

E) Infinitely Many Solutions

Step-by-step explanation:

A) 6(x+2)-10=6x+2

Simplify:

6 (x + 2) - 10 = 6x + 2

6x + 12 - 10 = 6x + 2

12 - 10 = 2

2 =2

Infinitely Many Solutions

B) 6(x+2)-12=6x+2

Simplify:

6 (x + 2) - 12 = 6x + 2

6x + 12 - 12 = 6x + 2

12 - 12 = 2

0 = 2

No Solution

C) 6(x+2)-10=2x+10

6 (x + 2) - 10 = 2x + 10

6x + 12 - 10 = 2x + 10

6x +2 = 2x + 10

4x = 8

x = 2

One Solution

D) 4x-2=4(x-2)+6

4x - 2 = 4 (x - 2) + 6

4x - 2 = 4x - 8 + 6

-2 = -8 + 6

-2 = -2

Infinitely Many Solutions

E) 2(3x-6)=6(-2+x)

2 (3x - 6) = 6 (-2 + x)

6x - 12 = -12 + 6x

6x = 6x

0 = 0

Infinitely Many Solutions