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What values of the variable cannot possibly be solutions for the given​ equation, without actually solving the​ equation? StartFraction 6 Over 2 x plus 3 EndFraction minus StartFraction 1 Over x minus 7 EndFraction equals 0 6 2x+3− 1 x−7=0 Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. The solutions cannot include nothing. ​(Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as​ needed.)
B. There are no numbers that would have to be rejected as potential solutions.

Respuesta :

Answer:

C. x=-1 and x=7

MrRoyal

The possible solutions of an equation are the values that can make the equation have real solutions.

The solutions cannot include -1.5 and 7.

Given that:

[tex]\frac{6}{2x + 3} - \frac{1}{x - 7}= 0[/tex]

To determine the values of x that cannot be a solution, we simply equate the denominator of both fractions to 0.

So, we have;

[tex]2x +3 = 0[/tex]

[tex]2x =-3[/tex]

Divide by 2

[tex]x = -1.5[/tex]

[tex]x - 7 = 0[/tex]

[tex]x = 7[/tex]

This means that option (A) is correct and the solutions cannot include -1.5 and 7.

Read more about solutions of equations at:

https://brainly.com/question/4024717

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