Question

-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 answer: Choose 1 answer: (Choice A) A No solutions (Choice B) B Exactly one solution (Choice C) C Infinitely many solutions

Answer 1

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:

$2x =x+3$

When we solve this:

$2x-x=3\\\Rightarrow x=3$

One solution is $x = 3$

But there can be situations when there are

1. No solutions:

For example:

$x =x+9$

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:

$x+2x+8=3x+8$

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 $x$.

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:

$-4x-7+10x=-7+6x$

Taking LHS: $-4x-7+10x$

Taking the terms with $x$ on one side:

$-7+10x-4x\\\Rightarrow -7+6x$

which is equal to Right Hand Side.

Hence, as we discussed in case 2 above.

For every value of $x$ the equation holds true.

$\therefore$ There exists infinitely many solutions to the given equation.

Correct answer is:

(Choice C) C Infinitely many solutions