Question

Can someone please help me??

Answer 1

I is clear that, the linear equation
`5x+12=5x-7` has no solution.

Explanation:

Checking the first option:

`(2)/(3)\left(9x+6\right)=6x+4`

`6x+4=6x+4`

`\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}`

`6x+4-4=6x+4-4`

`6x=6x`

`\mathrm{Subtract\:}6x\mathrm{\:from\:both\:sides}`

`6x-6x=6x-6x`

`0=0`

`\mathrm{Both\:sides\:are\:equal}`

`\mathrm{True\:for\:all}\:x`

Checking the 2nd option:

`5x+12=5x-7`

`\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}`

`5x+12-5x=5x-7-5x`

`\mathrm{Simplify}`

`12=-7`

`\mathrm{The\:sides\:are\:not\:equal}`

`\mathrm{No\:Solution}`

Checking the 3rd option:

`4x+7=3x+7`

`\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}`

`4x+7-7=3x+7-7`

`\mathrm{Simplify}`

`4x=3x`

`\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}`

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

`\mathrm{Simplify}`

`x=0`

Checking the 4th option:

`-3\left(2x-5\right)=15-6x`

`\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}`

`-6x+15-15=15-6x-15`

`\mathrm{Simplify}\`

`-6x=-6x`

`\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}`

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

`\mathrm{Simplify}`

`\mathrm{Both\:sides\:are\:equal}`

`\mathrm{True\:for\:all}\:x`

Result:

Therefore, from the above calculations it is clear that, the linear equation

`5x+12=5x-7` has no solution.