https://file.aiquickdraw.com/mathbot/file/1726523021799369okpi1.jpg

The given equation is:

\[
\frac{4}{7}x + \frac{1}{3}x = 38
\]

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

### Step 1: Combine like terms.
Both terms on the left-hand side of the equation involve \( x \). Combine them by finding a common denominator for the fractions \( \frac{4}{7} \) and \( \frac{1}{3} \).

The least common denominator (LCD) of 7 and 3 is 21.

Rewrite the fractions with the common denominator of 21:

\[
\frac{4}{7} = \frac{12}{21}, \quad \frac{1}{3} = \frac{7}{21}
\]

Now combine the fractions:

\[
\frac{12}{21}x + \frac{7}{21}x = \frac{12 + 7}{21}x = \frac{19}{21}x
\]

### Step 2: Solve the equation.
Now the equation is:

\[
\frac{19}{21}x = 38
\]

Multiply both sides of the equation by the reciprocal of \( \frac{19}{21} \), which is \( \frac{21}{19} \):

\[
x = 38 \times \frac{21}{19}
\]

### Step 3: Simplify the right-hand side.
First, simplify \( \frac{38}{19} \):

\[
38 \div 19 = 2
\]

Now multiply by 21:

\[
x = 2 \times 21 = 42
\]

### Final Answer:
\[
x = 42
\]

Would you like further clarification on any of these steps?

Here are 5 related questions for further practice:
1. Solve \( \frac{5}{8}x + \frac{3}{4}x = 16 \).
2. Solve \( \frac{7}{9}x - \frac{2}{3}x = 10 \).
3. If \( \frac{1}{2}x + \frac{2}{5}x = 12 \), what is the value of \( x \)?
4. How would you solve \( \frac{3}{4}x + \frac{5}{6}x = 50 \)?
5. Find \( x \) if \( \frac{9}{10}x - \frac{4}{5}x = 7 \).

**Tip:** When dealing with fractions in equations, always find the least common denominator to simplify the process of combining terms.

Learn how to solve the linear equation (4/7)x + (1/3)x = 38 using step-by-step fraction simplification and combining like terms. This problem involves algebraic concepts of linear equations and fractions, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation