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.