https://file.aiquickdraw.com/mathbot/file/17301960249439ztxphbh.jpg

The equation in the image is:

\[
\frac{t + 1}{3} - \frac{t + 2}{5} = 1
\]

To solve for \( t \), follow these steps:

### Step 1: Find a common denominator
The denominators are 3 and 5. The least common multiple of 3 and 5 is 15. Rewrite each term with a denominator of 15:

\[
\frac{t + 1}{3} = \frac{5(t + 1)}{15} = \frac{5t + 5}{15}
\]
\[
\frac{t + 2}{5} = \frac{3(t + 2)}{15} = \frac{3t + 6}{15}
\]

Now the equation becomes:
\[
\frac{5t + 5}{15} - \frac{3t + 6}{15} = 1
\]

### Step 2: Combine the fractions
Since both terms have a common denominator, combine them:

\[
\frac{(5t + 5) - (3t + 6)}{15} = 1
\]

Simplify the numerator:

\[
\frac{5t + 5 - 3t - 6}{15} = 1
\]
\[
\frac{2t - 1}{15} = 1
\]

### Step 3: Clear the fraction by multiplying both sides by 15

\[
2t - 1 = 15
\]

### Step 4: Solve for \( t \)

Add 1 to both sides:

\[
2t = 16
\]

Now, divide by 2:

\[
t = 8
\]

### Final Answer
\[
t = 8
\]

Would you like more details on any step, or do you have further questions?

---

Here are 5 related questions to explore further:

1. How do we determine the least common multiple of two numbers?
2. Why is it important to clear fractions when solving equations?
3. How can we verify that \( t = 8 \) is a solution to the original equation?
4. What are other methods to solve equations with fractions?
5. How does changing the terms on the right side affect the solution process?

**Tip:** When solving equations with fractions, always look for the least common denominator to simplify calculations.

Solve the equation \( \frac{t + 1}{3} - \frac{t + 2}{5} = 1 \).

Learn how to solve the algebraic fraction equation \( \frac{t + 1}{3} - \frac{t + 2}{5} = 1 \) with a step-by-step solution, covering key concepts such as finding a common denominator and simplifying equations with fractions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation