Question

Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
1/4 x^3 = -27/4





5
±5
Answer
can you do it without all the slashes and symbols
Answered by GPT-4o mini
To solve the equation

\[
\frac{1}{4} x^3 = -\frac{27}{4},
\]

we can start by isolating \(x^3\) using inverse operations. Here are the steps to solve it:

1. **Eliminate the fraction by multiplying both sides by 4**:
\[
4 \left(\frac{1}{4} x^3\right) = 4 \left(-\frac{27}{4}\right).
\]
This simplifies to:
\[
x^3 = -27.
\]

2. **Use the cube root to solve for \(x\)**:
\[
x = \sqrt[3]{-27}.
\]
Since the cube root of -27 is -3, we have:
\[
x = -3.
\]

3. **Check the solution** by substituting \(x = -3\) back into the original equation:
\[
\frac{1}{4} (-3)^3 = \frac{1}{4} (-27) = -\frac{27}{4}.
\]
Since both sides are equal, the solution is verified.

So, the final answer is:

\[
\boxed{-3}.
\]
Answered by GPT-4o mini
Sure! Here's how to solve the equation step by step without using slashes and symbols:

We begin with the equation:

**One-fourth of x cubed equals negative twenty-seven over four.**

1. To eliminate the fraction, multiply both sides of the equation by 4:

**4 times (one-fourth of x cubed) equals 4 times (negative twenty-seven over four).**

This simplifies to:

**x cubed equals negative twenty-seven.**

2. Next, to find x, we take the cube root of both sides:

**The cube root of x cubed equals the cube root of negative twenty-seven.**

This gives us:

**x equals negative three.**

3. Now, let's check our solution by substituting negative three back into the original equation:

**One-fourth of (negative three) cubed equals negative twenty-seven over four.**

Calculating:

**One-fourth of negative twenty-seven equals negative twenty-seven over four.**

Since both sides match, our solution is verified.

Therefore, the final answer is:

**x equals negative three.**