To solve the equation:

\[
\left(\frac{2x + 3}{6}\right)^6 = \left(\frac{3x + 1}{6}\right)^6
\]

We can start by taking the 6th root of both sides to simplify the equation:

\[
\frac{2x + 3}{6} = \frac{3x + 1}{6}
\]

Now, since the denominators are the same on both sides, we can equate the numerators:

\[
2x + 3 = 3x + 1
\]

Next, subtract \(2x\) from both sides:

\[
3 = x + 1
\]

Now, subtract 1 from both sides:

\[
x = 2
\]

Thus, the solution is:

\[
x = 2
\]

Would you like a detailed explanation of any specific step, or have any other questions?

Here are 5 related questions to expand your understanding:
1. What if the equation involved different powers, e.g., cubes instead of 6th powers?
2. How would you solve if the terms inside the parentheses were more complex?
3. What happens if one side of the equation has an extra constant term?
4. How does taking roots help simplify equations with powers?
5. What if the coefficients of \(x\) were fractions instead of integers?

**Tip**: When solving equations with powers on both sides, simplify by eliminating the powers early on using roots, if possible.

Discover how to solve the exponent equation ((2x+3)/6)^6 = ((3x+1)/6)^6 with a straightforward step-by-step approach. This problem emphasizes key algebraic concepts, such as simplifying equations using exponentiation and solving linear equations. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation