Respuesta :
6x+1=2(x+3)+4x has no solution because if you simplify it you get 6x+1=6x+3 which can not have any solution, since anything you substitute for x will not give you a solution.
4x-1=4(x+3) also has no solution. if you simplify you get 4x-1=4x+3 so no value that you substitute for x will give you a solution
4x-1=4(x+3) also has no solution. if you simplify you get 4x-1=4x+3 so no value that you substitute for x will give you a solution
Answer: The correct options are
(B) [tex]6x+1=2(x+3)+4x[/tex]
(D) [tex]4x-1=4(x+3)[/tex]
Step-by-step explanation: We are given to choose all the linear equations that have no solution.
To find the number of solutions, we must solve the equations first.
(A) The given equation is
[tex]2(x+5)-7=3(x-2)\\\\\Rightarrow 2x+10-7=3x-2\\\\\Rightarrow 2x+3=3x-2\\\\\Rightarrow 3x-2x=3+2\\\\\Rightarrow x=5.[/tex]
So, this equation has one solution.
Option (A) is not correct.
(B) The given equation is
[tex]6x+1=2(x+3)+4x\\\\\Rightarrow 6x+1=2x+6+4x\\\\\Rightarrow 6x+1=6x+6\\\\\Rightarrow 1=6,[/tex] not true.
So, this equation has no solution.
Option (B) is CORRECT.
(C) The given equation is
[tex]5x+10=5(x+2)\\\\\Rightarrow 5x+10=5x+10\\\\\Rightarrow 0=0,[/tex] which is always true.
So, this equation has infinite number of solutions.
Option (C) is not correct.
(D) The given equation is
[tex]4x-1=4(x+3)\\\\\Rightarrow 4x-1=4x+12\\\\\Rightarrow -1=12,[/tex] not true.
So, this equation will have no solution.
Option (D) is CORRECT.
(E) The given equation is
[tex]3(2x+4)=8x+12-2x\\\\\Rightarrow 6x+12=6x+12\\\\\Rightarrow 12=12,[/tex] which is always true.
So, this equation will have infinite number of solutions.
Option (E) is not correct.
Thus, (B) and (D) are the correct options.
