Question

Choose all of the linear equations that have no solution.

2(x + 5) − 7 = 3(x − 2)

6x + 1 = 2(x + 3) + 4x

5x + 10 = 5(x + 2)

4x − 1 = 4(x + 3)

3(2x + 4) = 8x + 12 − 2x

Answer 1

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

Answer 2

Answer: The correct options are

(B)
`6x+1=2(x+3)+4x`

(D)
`4x-1=4(x+3)`

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

`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.`

So, this equation has one solution.

Option (A) is not correct.

(B) The given equation is

`6x+1=2(x+3)+4x\\\\\Rightarrow 6x+1=2x+6+4x\\\\\Rightarrow 6x+1=6x+6\\\\\Rightarrow 1=6,` not true.

So, this equation has no solution.

Option (B) is CORRECT.

(C) The given equation is

`5x+10=5(x+2)\\\\\Rightarrow 5x+10=5x+10\\\\\Rightarrow 0=0,` which is always true.

So, this equation has infinite number of solutions.

Option (C) is not correct.

(D) The given equation is

`4x-1=4(x+3)\\\\\Rightarrow 4x-1=4x+12\\\\\Rightarrow -1=12,` not true.

So, this equation will have no solution.

Option (D) is CORRECT.

(E) The given equation is

`3(2x+4)=8x+12-2x\\\\\Rightarrow 6x+12=6x+12\\\\\Rightarrow 12=12,` 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.