Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.

Question

1/4 x^3 = -27/4


5
±5

Answer 1

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:

\[ \boxed{-3}. \]

Answer 2

can you do it without all the slashes and symbols

Answer 3

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.