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

x^2=81/144

(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

1 answer

To solve the equation \( x^2 = \frac{81}{144} \), we can first simplify the fraction on the right side:

\[ \frac{81}{144} = \frac{9}{16} \]

Now, the equation is:

\[ x^2 = \frac{9}{16} \]

To solve for \( x \), we take the square root of both sides. When taking the square root of both sides of an equation, we must remember that there are typically two solutions for \( x \) (one positive and one negative):

\[ x = \pm \sqrt{\frac{9}{16}} = \pm \frac{3}{4} \]

Thus, the statement options that are true when solving for \( x \) in the equation \( x^2 = \frac{81}{144} \) are:

  1. You would use the inverse operation of square root.
  2. There would be two solutions for \( x; x = \frac{3}{4} \) and \( x = -\frac{3}{4} \).

So, you would select these two responses:

  • You would use the inverse operation of square root.
  • There would be two solutions for x; x = 9/12 = +3/4 and x = -9/12 = -3/4.