If you cube a positive number, is the result positive or negative? What about cubing a negative number? Use this to decide whether $x$ must be positive or negative.

Ignore the negative sign and focus on $27$. Which small integer, when multiplied by itself three times, gives $27$?

Once you pick a value from the choices, actually cube it (multiply it by itself three times) and see if you get $-27$.

In Desmos, type y = x^3 + 27. This rewrites $x^3 = -27$ as $x^3 + 27 = 0$, so the solutions are where the graph crosses the $x$-axis.

Look for the point where the graph crosses the $x$-axis (where $y = 0$). Click on that intersection point; the $x$-coordinate shown is the value of $x$ that solves the original equation.

The equation $x^3 = -27$ asks: "What number $x$ multiplied by itself three times equals $-27$?" In other words, find $x$ so that $x \times x \times x = -27$.

If you cube a positive number (like $3$), the result is positive (for example, $3^3 = 3 \times 3 \times 3 = 27$). If you cube a negative number (like $-3$), the result is negative (for example, $(-3)^3 = -27$).

Because the right side of the equation is $-27$ (a negative number), $x$ must be negative.

Ignore the negative sign for a moment and think about the size:

We want $|x|^3 = 27$. Try small integers:

• $2^3 = 8$
• $3^3 = 27$

So $|x| = 3$.

From Step 2, $x$ must be negative. From Step 3, $|x| = 3$. Combining these, $x = -3$.

So the value of $x$ that satisfies $x^3 = -27$ is $-3$ (choice B).