https://file.aiquickdraw.com/mathbot/file/1727312232269zqcmta3n.jpg

The equation shown in the image is:

\[
10y^3 + 6 = 146
\]

Let's solve for \( y \).

### Step 1: Subtract 6 from both sides to isolate the cubic term.

\[
10y^3 = 146 - 6
\]
\[
10y^3 = 140
\]

### Step 2: Divide both sides by 10.

\[
y^3 = \frac{140}{10}
\]
\[
y^3 = 14
\]

### Step 3: Take the cube root of both sides to solve for \( y \).

\[
y = \sqrt[3]{14}
\]

Thus, the solution is:

\[
y \approx 2.410
\]

Would you like further details on the cube root step or additional explanations?

Here are some related questions to deepen your understanding:
1. How can we check if our solution is correct by substituting back into the original equation?
2. What are the general steps to solve cubic equations like this one?
3. Can a cubic equation have more than one solution?
4. How can we solve the equation if the numbers were not as simple, such as involving complex roots?
5. What would happen if the cubic term had a negative coefficient?

**Tip:** Always isolate the highest power of the variable before solving an equation involving powers or roots.

Learn how to solve the cubic equation 10y^3 + 6 = 146 with a step-by-step breakdown. This problem involves isolating the cubic term, solving for y, and using the cube root to find the solution. Suitable for high school algebra students in Grades 9-12.

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