Question

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

Answer 1

$6x + 9$
I am pretty sure that would be the answer.

Answer 2

Answer:

No solution:.

We get a no solution when the linear equality give some absurd results.

Hence, let us suppose we write the given equality as:

2x+9+3x+x=6x+10

since,

on solving this equality we get:

2x+3x+x+9=6x+10  ( on combining like terms in the left hand side of the equality)

6x+9=6x+10  

6x-6x=10-9  ( on taking the variable terms to one side of the equation and constant term to other side)

0=1

which is absurd.

Hence, we get a No solution.

One solution:

one solution means that on solving the linear equality we get a unique value for our variable x and hence the solution is also called a unique solution.

We will write our equation as:

2x+9+3x+x=2x+17

on solving:

2x+3x+x+9=2x+17

6x+9=2x+17

6x-2x=17-9

4x=8

x=2.

Hence, we get a unique solution.

Infinitely many solution:

Infinite many solution means that the equation will hold true for infinitely many values of 'x' i.e we do not get a unique value.

so,

2x+9+3x+x=6x+9

2x+3x+x=6x+9

6x+9=6x+9

6x-6x=9-9

0=0

Hence, we can get infinite values or our x.