Question

Which linear equations have an infinite number of solutions? Check all that apply. (x – ) = (x – )8(x + 2) = 5x – 1412.3x – 18 = 3(–6 + 4.1x)(6x + 10) = 7(x – 2)4.2x – 3.5 = 2.1 (5x + 8)

Answer 1

To know if a expression have infinite solution we replace x for the same values in bot sides so I will replace x=0 in all option so:

a)

`\begin{gathered} (0-(3)/(7))=(2)/(3)((3)/(2)(0)-(9)/(14)) \\ -(3)/(7)=-(18)/(42) \\ -(3)/(7)=-(3)/(7) \end{gathered}`

So there are infinit solutions.

b)

`\begin{gathered} 8(0+2)=5(0)-14 \\ 16=-14 \end{gathered}`

so this do NOT have infinite solutions.

c)

`\begin{gathered} 12.3(0)-18=3(-6+4.1(0)) \\ -18=-18 \end{gathered}`

SO it has infinite solutions

d)

`\begin{gathered} (1)/(2)(6(0)+10)=7((3)/(7)(0)-2) \\ 5=-14 \end{gathered}`

So this do NOT have infinit solutions

e)

`\begin{gathered} 4.2(0)-3.5=2.1(5(0)+8) \\ -3.5=18.8 \end{gathered}`

SO it do NOT have infinite solutions

So A) and C) have infinite solutions