Answer:
1. [tex]7, a,\ a\neq 2[/tex] (for example, 7, 1);
2. [tex]b,\ b\neq 7,\ a;[/tex] (for example, 5, 6);
3. [tex]7,\ 2.[/tex]
Step-by-step explanation:
Simplify the given left side of each equation:
[tex]5-4+7x+1=7x+(5-4+1)=7x+2.[/tex]
The equation
- has no solution if it is impossible for the equation to be true no matter what value we assign to the variable x;
- has infinitely many solutions if any value for the variable x would make the equation true;
- has exactly one solution.
No solutions: The right side of the equation should be of the form [tex]7x+a,[/tex] where [tex]a\neq 2.[/tex] For example, [tex]7x+1.[/tex] In this case, the equation will take look
[tex]7x+2=7x+1,\\ \\ 2=1.[/tex]
This statement cannot be correct for any value of the variable x, so the equation has no solutions.
Infinitely many solutions: The right side should be exactly the same as the left side:
[tex]7x+2=7x+2,\\ \\0=0.[/tex]
This statement is correct for all values of the variable x, so the equation has infinitely many solutions.
One solution: The right side of the equation should be of the form [tex]bx+a,[/tex] where [tex]b\neq 7.[/tex] For example, [tex]5x+6.[/tex] In this case,
[tex]7x+2=5x+6,\\ \\7x-5x=6-2,\\ \\2x=4,\\ \\x=2.[/tex]
