Question

Solve $x^{2}=\frac {16}{25}$ by inspection. There are two real solutions. Enter the lesser number first.Leave
the answers in simplest fraction form. (1 point)
$\{ \square ,\square \} $

Answer 1

To solve the equation \( x^{2} = \frac{16}{25} \) by inspection, we will take the square root of both sides.

Starting with the equation:

\[
x^{2} = \frac{16}{25}
\]

Taking the square root of both sides, we get:

\[
x = \pm \sqrt{\frac{16}{25}}
\]

Using the property of square roots, we can rewrite this as:

\[
x = \pm \frac{\sqrt{16}}{\sqrt{25}} = \pm \frac{4}{5}
\]

This gives us two solutions:

\[
x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5}
\]

Now, we are required to write the lesser number first:

The lesser solution is \( -\frac{4}{5} \) and the greater solution is \( \frac{4}{5} \).

Thus, the solutions are:

\[
\{ -\frac{4}{5}, \frac{4}{5} \}
\]

So, the final answer is:

\[
\{ -\frac{4}{5}, \frac{4}{5} \}
\]