Solve for t.
–
4

3
t+
1

2
=
3

2
–2t+
5

3
t

The equation you provided is:

\[
\frac{4}{3} t + \frac{1}{2} = \frac{3}{2} - 2t + \frac{5}{3} t
\]

### Step-by-step Solution:

1. **Multiply through by a common denominator** to eliminate the fractions. The least common denominator (LCD) of 3, 2, and 3 is 6.

\[
6 \left(\frac{4}{3} t + \frac{1}{2} \right) = 6 \left( \frac{3}{2} - 2t + \frac{5}{3} t \right)
\]

Simplifying each term:

\[
6 \times \frac{4}{3} t = 8t, \quad 6 \times \frac{1}{2} = 3
\]
\[
6 \times \frac{3}{2} = 9, \quad 6 \times (-2t) = -12t, \quad 6 \times \frac{5}{3} t = 10t
\]

So the equation becomes:

\[
8t + 3 = 9 - 12t + 10t
\]

2. **Combine like terms** on the right side:

\[
9 - 12t + 10t = 9 - 2t
\]

So the equation is now:

\[
8t + 3 = 9 - 2t
\]

3. **Move all the terms involving \( t \) to one side** and constants to the other side:

\[
8t + 2t = 9 - 3
\]

Simplifying:

\[
10t = 6
\]

4. **Solve for \( t \):**

\[
t = \frac{6}{10} = \frac{3}{5}
\]

### Final Answer:
\[
t = \frac{3}{5}
\]

Do you want further details or have any questions?

---

Here are 5 questions related to solving similar types of equations:
1. How do you find the least common denominator of multiple fractions?
2. What are some strategies to simplify equations with multiple fractions?
3. How can you check if your solution to a linear equation is correct?
4. What happens if the variable cancels out on both sides of the equation?
5. How do you solve an equation with variables on both sides?

**Tip:** Always remember to double-check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Solve for t.

\(\frac{4}{3}t + \frac{1}{2} = \frac{3}{2} - 2t + \frac{5}{3}t\)

Learn how to solve the linear equation with fractions: 4/3 t + 1/2 = 3/2 - 2t + 5/3 t. This step-by-step solution covers key algebraic concepts, including finding a common denominator and solving for the variable t. Ideal for students in Grades 8-10.

Math Problem Statement

2

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation