Q:

Use the drop-down menus to complete each equation so the statement about its solution is truenumbers in the drop box range from 0-9

Accepted Solution

A:
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 equationhas 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: Β  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]