Question

Use the drop-down menus to complete each equation so the statement about its solution is true

Answer 1

Answer:

1. $7, a,\ a\neq 2$ (for example, 7, 1);

2. $b,\ b\neq 7,\ a;$ (for example, 5, 6);

3. $7,\ 2.$

Step-by-step explanation:

Simplify the given left side of each equation:

$5-4+7x+1=7x+(5-4+1)=7x+2.$

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 $7x+a,$ where $a\neq 2.$ For example, $7x+1.$ In this case, the equation will take look

$7x+2=7x+1,\\ \\ 2=1.$

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:

$7x+2=7x+2,\\ \\0=0.$

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 $bx+a,$ where $b\neq 7.$ For example, $5x+6.$ In this case,

$7x+2=5x+6,\\ \\7x-5x=6-2,\\ \\2x=4,\\ \\x=2.$