-4x-7+10x=-7+6x−4x−7+10x=−7+6xminus , 4, x, minus, 7, plus, 10, x, equals, minus, 7, plus, 6, x Choose 1 Choose 1 (Choice A) A No solutions (Choice B) B Exactly one solution (Choice C) C Infinitely many solutions

(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

But there can be situations when there are

1. No solutions:

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.

2. Infinitely many solutions:

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:

(Choice C) C Infinitely many solutions

christopher is 272,195 year old

step-by-step explanation:

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116