Question

Do only equations with variables on both sides have no​ solution? Or can the variable be just on one​ side? Justify your answer.
Choose the correct answer below.
A.
Any equation can have one​ solution, infinitely many​ solutions, or no solutions. This does not depend on whether the variable appears on only one side or on both sides.
B.
Every equation with variables on both sides has no solution.​ However, it is also possible for an equation with the variable on only one side to also have no solution.
C.
If the variable only appears on one side of an​ equation, then the equation can always be solved for the variable. By​ contrast, an equation with variables on both sides always has no solution or infinitely many solutions.
D.
If the variable only appears on one side of an​ equation, then the equation can always be solved for the variable. This means that if an equation has no​ solution, then the variable must appear on both sides.

Answer 1

Answer:

A

Step-by-step explanation:

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Answer 2

The number of solutions, an equation can have is independent of the position of the variable.

An equation can have:

• 1 solution
• Infinitely many solutions
• No solutions

Irrespective of where the variable appears

Take for instance:

$x + 5 = 17 - x$

To solve this, we start by collecting like terms

$x + x = 17- 5$

$2x = 12$

Divide both sides by 2

$x = 6$

In the above scenario, the variable (x) appears on both sides of the equation and the equation has 1 solution.

Another case scenario is as follows:

$x + 5 = x$

Collect like term

$x - x = -5$

$0 = -5$

The above scenario shows that the equation has no solution and the variable (x) appears on both sides of the equation.

So, we can conclude that, an equation can have:

• 1 solution
• Infinitely many solutions
• No solutions

Irrespective of where the variable appears

Hence, option (a) is correct.

Read more about solutions to equations at:

https://brainly.com/question/2560090