Let's solve the expression step by step:

Expression: 

\[
\frac{2}{3} + 3x + 4\left(x + \frac{5}{3}\right) - 4
\]

### Step 1: Distribute the \(4\) across the terms inside the parentheses.
\[
4\left(x + \frac{5}{3}\right) = 4x + \frac{20}{3}
\]

So, the expression becomes:
\[
\frac{2}{3} + 3x + 4x + \frac{20}{3} - 4
\]

### Step 2: Combine like terms.

- Combine the constants involving fractions: 
\[
\frac{2}{3} + \frac{20}{3} = \frac{22}{3}
\]
- Combine the \(x\)-terms:
\[
3x + 4x = 7x
\]

Now the expression becomes:
\[
\frac{22}{3} + 7x - 4
\]

### Step 3: Simplify further by combining the constants:

To combine \(\frac{22}{3}\) and \(-4\), convert \(-4\) to a fraction:
\[
-4 = \frac{-12}{3}
\]

So:
\[
\frac{22}{3} - \frac{12}{3} = \frac{10}{3}
\]

### Final expression:
\[
\frac{10}{3} + 7x
\]

This is the simplified form of the given expression.

Do you have any questions or would you like further clarification?

### Related questions:
1. How do you handle parentheses and distribution in an algebraic expression?
2. What are some techniques to combine fractions in algebra?
3. How do you convert whole numbers to fractions when simplifying expressions?
4. Can you solve for \(x\) in linear equations like this one?
5. What are common strategies to check if an expression is simplified?

### Tip:
Always combine like terms (constants, \(x\)-terms, etc.) step by step to simplify algebraic expressions efficiently.

Solve the algebraic expression 2/3 + 3x + 4(x + 5/3) - 4 step by step. This guide covers key concepts in algebra such as distribution, combining like terms, and working with fractions. Ideal 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