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Which statement is true when you solve for x ?

x^2=9/121 (1 point)
Responses

You would use the inverse operation of dividing both sides by 2; there would be one solution for x; x=960.5You would use the inverse operation of dividing both sides by 2; there would be one solution for x; x is equal to 9 over 60 point 5

You would use the inverse operation of square root; there would be one solution for x; x=311You would use the inverse operation of square root; there would be one solution for x; x is equal to 3 over 11

You would use the inverse operation of dividing both sides by 2; there would be one solution for x; x=4.5121You would use the inverse operation of dividing both sides by 2; there would be one solution for x; x is equal to 4 point 5 over 121

You would use the inverse operation of square root; there would be two solutions for x; x=311 and x = −311You would use the inverse operation of square root; there would be two solutions for x; x=311 and x = −311

1 answer

To solve the equation \( x^2 = \frac{9}{121} \), you would use the inverse operation of taking the square root.

  1. Taking the square root of both sides gives: \[ x = \pm \sqrt{\frac{9}{121}} \]

  2. Simplifying the square root: \[ x = \pm \frac{\sqrt{9}}{\sqrt{121}} = \pm \frac{3}{11} \]

Therefore, the solution for x is: \[ x = \frac{3}{11} \quad \text{and} \quad x = -\frac{3}{11} \]

The correct option is:

  • You would use the inverse operation of square root; there would be two solutions for x; \( x = \frac{3}{11} \) and \( x = -\frac{3}{11} \)