Question

10-12 please help, find the missing number and once you found the missing number and answered it you make sure it’s the solution it gave you like 10:infinitely many solutions

Answer 1

10. Infinitely many solutions:

`2(x-1)+6x=4(?-1)+2.`

Simplify this equation:

`2x-2+6x=4\cdot ?-4+2,\\ \\8x-2=4\cdot ? -2,\\ \\8x=4\cdot ?`

When
`?=2x,` the equation becomes

`8x=8x \text{ or } 0=0.`

This equality is true for all x, thus the equation has infinitely many solutions.

11. The equation
`5x-(x-2)=2x-(?)` should have one solution x=-1.

First, simplify the equation:

`5x-x+2=2x-?,\\ \\4x+2=2x-?,\\ \\2x+2=-?,\\ \\?=-2x-2.`

This equation will have solution x=-1 when

`?=-2\cdot (-1)-2=2-2=0.`

Therefore, the initial equation is

`5x-(x-2)=2x.`

12. The equation
`-(x-8)+4x=2\cdot ?+x` should have infinitely many solutions.

Simplify it:

`-x+8+4x=2\cdot ?+x,\\ \\2x+8=2\cdot ?,\\ \\2(x+4)=2\cdot ?.`

When
`?=x+4,` this equation will have infinitely many solutions.