Answer:
(Choice C) C Infinitely many solutions.
Step-by-step explanation:
First of all, let us learn about solutions of linear equations in one variable.
The linear equations in one variable usually have one solution.
For example:
When we solve this:
One solution is
<em>But there can be situations when there are</em>
<u>1.</u><u> </u><u>No solutions:</u>
For example:
It means that value x is equal to value of x+9 which can never be true.
Truth is the term on Right Hand Side is always 9 greater than the value of Left Hand Side.
Such situations are called Contradictions.
Here, no solution exists.
<u>2. Infinitely many solutions:</u>
For example:
The Right hand Side is just the simplification of the LHS.
And LHS is always equal to RHS no matter what is the value of variable .
It means there are infinitely many solutions for this equation.
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Now, let us have a look at the given equation in the question:
Taking LHS:
Taking the terms with on one side:
which is equal to Right Hand Side.
Hence, as we discussed in case 2 above.
For every value of the equation holds true.
There exists infinitely many solutions to the given equation.
Correct answer is:
<em>(Choice C) C Infinitely many solutions</em>