How many solutions does 6(x + 7) = 3(2x + 14) have

Question

just please solve this it's really bothering me

Answer 1

6(x+7) = 3(2x + 14)

6x + 42 = 6x + 42

42 = 42

 

Therefore, it has an infinite number of solutions because any number you put in for x will make a true equation.  

 

EX.  x = 2

6(2+7) = 3(2*2+14)

6(9) = 3(18)

54 = 54

 

x = -1

6(-1 + 7) = 3(2*-1 + 14)

6(6) = 3(12)

36=36

Answer 2

Theoretically, linear equations have only one solution.  But don't be fooled.  We should expand both sides of the equation using distributive property.

 

6x + 42 = 6x + 42

 

 

Since the left and right side are exactly the same, the equation has infinite solutions.  Graphical, you has two identical lines overlapping.