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Which statement(s) true when solving the equation for x ? CHOOSE TWO.

x2=81144

(2 points)
Responses

You would use the inverse operation of dividing both sides by 2
You would use the inverse operation of dividing both sides by 2

You would use the inverse operation of square root
You would use the inverse operation of square root

You would use the inverse operation of multiplying both sides by itself
You would use the inverse operation of multiplying both sides by itself

You would use the inverse operation of dividing both sides by 4
You would use the inverse operation of dividing both sides by 4

There is no solution for x in this equation.
There is no solution for x in this equation.

there would be one solution for x;

x = 81/72 = 9/8

there would be one solution for x; x = 81/72 = 9/8

there would be two solutions for x;

x = 9/12 = +3/4 and x = - 9/12 = - 3/4

there would be two solutions for x; x = 9/12 = +3/4 and x = - 9/12 = - 3/4

there would be one solution for x;

x = 9/12 = 3/4

there would be one solution for x; x = 9/12 = 3/4

there would be two solutions for x;

x = 81/72 = 9/8 and x = - 81/72 = -9/8

there would be two solutions for x; x = 81/72 = 9/8 and x = - 81/72 = -9/8

1 answer

To solve the equation \( x^2 = 81144 \), let's analyze the statements regarding the operations needed and the potential solutions:

  1. You would use the inverse operation of square root. - True: To isolate \( x \), you take the square root of both sides of the equation since \( x \) is squared.

  2. You would use the inverse operation of dividing both sides by 2. - False: This operation is not relevant to this equation since the equation does not involve division by 2.

  3. You would use the inverse operation of multiplying both sides by itself. - False: This statement is misleading; you wouldn't multiply both sides by themselves; rather, you would take the square root of one side.

  4. You would use the inverse operation of dividing both sides by 4. - False: This is not applicable to this equation.

  5. There is no solution for x in this equation. - False: There are solutions since \( 81144 \) is a positive number.

  6. There would be one solution for x; x = 81/72 = 9/8. - False: This doesn't pertain to the actual solution of the equation.

  7. There would be two solutions for x; x = 9/12 = +3/4 and x = -9/12 = -3/4. - False: Not relevant to this equation.

  8. There would be one solution for x; x = 9/12 = 3/4. - False: Similar to previous, not related to this equation.

  9. There would be two solutions for x; x = 81/72 = 9/8 and x = -81/72 = -9/8. - False: Although it incorrectly cites the value, there are indeed two solutions for the correct equation.

The correct answers are:

  • You would use the inverse operation of square root.
  • There would be two solutions for x; (although the exact values aren't provided accurately in any option), the context implies two solutions exist due to squaring.

Therefore, the most correct pair of statements to choose are:

  • "You would use the inverse operation of square root."
  • "There would be two solutions for x; … (affirmative of solutions existing)."