Question

Select all the equations that have no solution and state your reasoning as of "why" they do not have a solution. +6=5+ x+6=5+x −2(−3)=-2+6 −2(x−3)=-2x+6 4−4=3+2 4−4x=3x+2 4(+1)=3(+2) 4(x+1)=3(x+2) 5−3=-3+4 5−3x=-3x+4

Answer 1

Equations:

`x+6=5+x`

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

`4-4x=3x+2`

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

`5-3x=-3x+4`

Answer:

`x+6=5+x`

`5-3x=-3x+4`

Explanation:

Given

`x+6=5+x`

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

`4-4x=3x+2`

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

`5-3x=-3x+4`

Required:

Which have no solution

`x+6=5+x`

Subtract x from both sides

`x -x+6 = 5 + x - x`

`6 = 5`

`x+6=5+x` has no solution because
`6 \\e 5`

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

Open bracket

`-2x + 6 = -2x + 6`

Both sides are equal.

Hence, there is an
`Infinite\ Number` of Solutions

`4-4x=3x+2`

Collect like terms

`-3x - 4x = 2 - 4`

`-7x = -2`

Solve for x

`x = (-2)/(-7)`

`x = (2)/(7)` --- This has a solution

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

Open brackets

`4x + 4 = 3x + 6`

Collect like terms

`4x-3x = 6 - 4`

`x = 2` --- This has a solution

`5-3x=-3x+4`

Add 3x to both sides

`5 - 3x + 3x = -3x + 3x + 4`

`5 = 4`

`5-3x=-3x+4` has no solution because
`5 \\e 4`